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If A, B and C are three consecutive points on the arc of a semi-circle such that the angles subtended by the chords AB and AC at the centre of the circle are 60 and 100 degrees respectively. The BOC is
  • a)
    30 degrees
  • b)
    50 degrees
  • c)
    25 degrees
  • d)
    15 degrees
  • e)
    40 degrees
Correct answer is option 'E'. Can you explain this answer?
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Most Upvoted Answer
If A, B and C are three consecutive points on the arc of a semi-circl...
∠ AOC = 100
∠ AOC = ∠ AOB + ∠ BOC
Therefore, ∠ BOC = 100 - 60 = 40 degrees.
Option E
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Community Answer
If A, B and C are three consecutive points on the arc of a semi-circl...
Given:
- A, B, and C are three consecutive points on the arc of a semicircle.
- The angles subtended by the chords AB and AC at the center of the circle are 60° and 100° respectively.

To find:
The measure of angle BOC.

Solution:
Let O be the center of the semicircle.

Step 1: Draw a diagram
- Draw a semicircle with center O.
- Mark three points A, B, and C on the arc of the semicircle.
- Join AB and AC to form chords.
- Draw a radius OC from the center O to the point C.

Step 2: Identify the given angles
- Angle BOA = 60° (angle subtended by chord AB at the center O)
- Angle COA = 100° (angle subtended by chord AC at the center O)

Step 3: Identify the angles in the triangle OAC
- Triangle OAC is an isosceles triangle because OA = OC (both are radii of the semicircle).
- Therefore, angle OAC = angle OCA.

Step 4: Calculate angle OAC
- In triangle OAC, angle OAC + angle OCA + angle COA = 180° (sum of angles in a triangle)
- Substitute the given values: angle OAC + angle OAC + 100° = 180°
- Simplify: 2 * angle OAC = 80°
- Divide both sides by 2: angle OAC = 40°

Step 5: Calculate angle BOC
- Angle BOC is the sum of angles BOA, OAC, and COA.
- Substitute the given values: angle BOC = 60° + 40° + 100° = 200°

Step 6: Convert angle BOC to its complementary angle
- Since BOC is an angle inside a semicircle, it is the complement of the angle subtended by the arc BC at the center O.
- The sum of complementary angles is 90°.
- Therefore, the complementary angle of 200° is 90° - 200° = -110°
- Since angles cannot be negative, we take the positive value: 110°

Step 7: Calculate the measure of angle BOC
- The measure of angle BOC is equal to the complementary angle of the angle subtended by the arc BC at the center O.
- Therefore, angle BOC = 180° - 110° = 70°

Conclusion:
The measure of angle BOC is 70°, which is not listed as one of the answer options. Therefore, there may be an error in the provided answer options.
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Directions: Read the following passage carefully and answer the questions that follow.Over the course of a single generation in South Korea, degrees have become close to ubiquitous. Seventy per cent of pupils who graduate from the country's secondary schools now go straight to university, and a similar share of 25- to 34-year-olds hold degrees, up from 37% in 2000. Students scramble to gain admittance to the most prestigious institutions, with exam preparation starting ever younger. Sought-after private nurseries in Seoul have long waiting lists.South Korea is an extreme case. But other countries, too, have seen a big rise in the share of young people with degrees. In the OECD club of 35 countries, 43% of 25- to 34-year-olds now have degrees. In America the figure is 48%. Between 1995 and 2014 government spending on higher education in the OECD rose from 0.9% of GDP to 1.1%, while private spending rose from 1.2% to 1.5%. As government subsidies for tuition fees flow through to institutions they have helped inflate costs. Since 1990 fees for American students who do not get scholarships or bursaries have risen twice as fast as overall inflation.Policymakers regard it as obvious that sending more young people to university will boost economic growth and social mobility. Both notions are intuitively appealing. Better-educated people should surely be more likely to come up with productivity-boosting innovations. As technological change makes new demands of workers, it seems plausible that more will need to be well-educated. And a degree is an obvious way for bright youngsters from poor families to prove their abilities. But comparisons between countries provide little evidence of these links. Richer countries have more graduates, but that could be because there is more money to spare, and less urgency to start earning. Rich economies grow more slowly, but that is probably because they have fewer easy ways to raise productivity, not because education depresses their growth.The main piece of evidence cited by policymakers is the "graduate premium" - the difference between the average earnings of someone with a degree and someone with no more than a secondary-school education, after accounting for fees and the income forgone while studying. This gap is often expressed as the "return on investment" in higher education, or the annualised boost to lifetime earnings from gaining a degree. Research by the New York Federal Reserve shows that the return on investment in higher education soared between 1980 and 2000 in America, before levelling off at around 15% a year. In other words, an investment equal to the cost of tuition and earnings forgone while studying would have to earn 15% annual interest before it matched the average value over a working life of gaining a degree.The World Bank has produced estimates of this return for 139 economies. It varies from place to place but is substantial everywhere. The returns are linked to the share of people with degrees, and the range of earnings. Returns in Britain and Germany are similar to those in America. In sub-Saharan Africa, where degrees are scarce, and the least-educated workers earn little, they are around 21% a year. In Scandinavia, where wages are less unequal, and two-fifths of adults have degrees, they are around 9%.Which country/group of countries have less unequal wages and two-fifths of adults have degrees?

Directions: Read the following passage carefully and answer the questions that follow.Over the course of a single generation in South Korea, degrees have become close to ubiquitous. Seventy per cent of pupils who graduate from the country's secondary schools now go straight to university, and a similar share of 25- to 34-year-olds hold degrees, up from 37% in 2000. Students scramble to gain admittance to the most prestigious institutions, with exam preparation starting ever younger. Sought-after private nurseries in Seoul have long waiting lists.South Korea is an extreme case. But other countries, too, have seen a big rise in the share of young people with degrees. In the OECD club of 35 countries, 43% of 25- to 34-year-olds now have degrees. In America the figure is 48%. Between 1995 and 2014 government spending on higher education in the OECD rose from 0.9% of GDP to 1.1%, while private spending rose from 1.2% to 1.5%. As government subsidies for tuition fees flow through to institutions they have helped inflate costs. Since 1990 fees for American students who do not get scholarships or bursaries have risen twice as fast as overall inflation.Policymakers regard it as obvious that sending more young people to university will boost economic growth and social mobility. Both notions are intuitively appealing. Better-educated people should surely be more likely to come up with productivity-boosting innovations. As technological change makes new demands of workers, it seems plausible that more will need to be well-educated. And a degree is an obvious way for bright youngsters from poor families to prove their abilities. But comparisons between countries provide little evidence of these links. Richer countries have more graduates, but that could be because there is more money to spare, and less urgency to start earning. Rich economies grow more slowly, but that is probably because they have fewer easy ways to raise productivity, not because education depresses their growth.The main piece of evidence cited by policymakers is the "graduate premium" - the difference between the average earnings of someone with a degree and someone with no more than a secondary-school education, after accounting for fees and the income forgone while studying. This gap is often expressed as the "return on investment" in higher education, or the annualised boost to lifetime earnings from gaining a degree. Research by the New York Federal Reserve shows that the return on investment in higher education soared between 1980 and 2000 in America, before levelling off at around 15% a year. In other words, an investment equal to the cost of tuition and earnings forgone while studying would have to earn 15% annual interest before it matched the average value over a working life of gaining a degree.The World Bank has produced estimates of this return for 139 economies. It varies from place to place but is substantial everywhere. The returns are linked to the share of people with degrees, and the range of earnings. Returns in Britain and Germany are similar to those in America. In sub-Saharan Africa, where degrees are scarce, and the least-educated workers earn little, they are around 21% a year. In Scandinavia, where wages are less unequal, and two-fifths of adults have degrees, they are around 9%.As per the passage, which of the following becomes possible as a result of better-educated people?I. Boosting economic growthII. Enhancing social mobilityIII. Coming up with productivity-boosting innovations

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Directions: Read the following passage carefully and answer the questions that follow.Over the course of a single generation in South Korea, degrees have become close to ubiquitous. Seventy per cent of pupils who graduate from the country's secondary schools now go straight to university, and a similar share of 25- to 34-year-olds hold degrees, up from 37% in 2000. Students scramble to gain admittance to the most prestigious institutions, with exam preparation starting ever younger. Sought-after private nurseries in Seoul have long waiting lists.South Korea is an extreme case. But other countries, too, have seen a big rise in the share of young people with degrees. In the OECD club of 35 countries, 43% of 25- to 34-year-olds now have degrees. In America the figure is 48%. Between 1995 and 2014 government spending on higher education in the OECD rose from 0.9% of GDP to 1.1%, while private spending rose from 1.2% to 1.5%. As government subsidies for tuition fees flow through to institutions they have helped inflate costs. Since 1990 fees for American students who do not get scholarships or bursaries have risen twice as fast as overall inflation.Policymakers regard it as obvious that sending more young people to university will boost economic growth and social mobility. Both notions are intuitively appealing. Better-educated people should surely be more likely to come up with productivity-boosting innovations. As technological change makes new demands of workers, it seems plausible that more will need to be well-educated. And a degree is an obvious way for bright youngsters from poor families to prove their abilities. But comparisons between countries provide little evidence of these links. Richer countries have more graduates, but that could be because there is more money to spare, and less urgency to start earning. Rich economies grow more slowly, but that is probably because they have fewer easy ways to raise productivity, not because education depresses their growth.The main piece of evidence cited by policymakers is the "graduate premium" - the difference between the average earnings of someone with a degree and someone with no more than a secondary-school education, after accounting for fees and the income forgone while studying. This gap is often expressed as the "return on investment" in higher education, or the annualised boost to lifetime earnings from gaining a degree. Research by the New York Federal Reserve shows that the return on investment in higher education soared between 1980 and 2000 in America, before levelling off at around 15% a year. In other words, an investment equal to the cost of tuition and earnings forgone while studying would have to earn 15% annual interest before it matched the average value over a working life of gaining a degree.The World Bank has produced estimates of this return for 139 economies. It varies from place to place but is substantial everywhere. The returns are linked to the share of people with degrees, and the range of earnings. Returns in Britain and Germany are similar to those in America. In sub-Saharan Africa, where degrees are scarce, and the least-educated workers earn little, they are around 21% a year. In Scandinavia, where wages are less unequal, and two-fifths of adults have degrees, they are around 9%.Which of the following could be the closest synonym of "forgone", as per the passage?

Directions: Read the following passage carefully and answer the questions that follow.Over the course of a single generation in South Korea, degrees have become close to ubiquitous. Seventy per cent of pupils who graduate from the country's secondary schools now go straight to university, and a similar share of 25- to 34-year-olds hold degrees, up from 37% in 2000. Students scramble to gain admittance to the most prestigious institutions, with exam preparation starting ever younger. Sought-after private nurseries in Seoul have long waiting lists.South Korea is an extreme case. But other countries, too, have seen a big rise in the share of young people with degrees. In the OECD club of 35 countries, 43% of 25- to 34-year-olds now have degrees. In America the figure is 48%. Between 1995 and 2014 government spending on higher education in the OECD rose from 0.9% of GDP to 1.1%, while private spending rose from 1.2% to 1.5%. As government subsidies for tuition fees flow through to institutions they have helped inflate costs. Since 1990 fees for American students who do not get scholarships or bursaries have risen twice as fast as overall inflation.Policymakers regard it as obvious that sending more young people to university will boost economic growth and social mobility. Both notions are intuitively appealing. Better-educated people should surely be more likely to come up with productivity-boosting innovations. As technological change makes new demands of workers, it seems plausible that more will need to be well-educated. And a degree is an obvious way for bright youngsters from poor families to prove their abilities. But comparisons between countries provide little evidence of these links. Richer countries have more graduates, but that could be because there is more money to spare, and less urgency to start earning. Rich economies grow more slowly, but that is probably because they have fewer easy ways to raise productivity, not because education depresses their growth.The main piece of evidence cited by policymakers is the "graduate premium" - the difference between the average earnings of someone with a degree and someone with no more than a secondary-school education, after accounting for fees and the income forgone while studying. This gap is often expressed as the "return on investment" in higher education, or the annualised boost to lifetime earnings from gaining a degree. Research by the New York Federal Reserve shows that the return on investment in higher education soared between 1980 and 2000 in America, before levelling off at around 15% a year. In other words, an investment equal to the cost of tuition and earnings forgone while studying would have to earn 15% annual interest before it matched the average value over a working life of gaining a degree.The World Bank has produced estimates of this return for 139 economies. It varies from place to place but is substantial everywhere. The returns are linked to the share of people with degrees, and the range of earnings. Returns in Britain and Germany are similar to those in America. In sub-Saharan Africa, where degrees are scarce, and the least-educated workers earn little, they are around 21% a year. In Scandinavia, where wages are less unequal, and two-fifths of adults have degrees, they are around 9%.Which of the following could be the closest antonym of "appealing", as used in the passage?

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If A, B and C are three consecutive points on the arc of a semi-circle such that the angles subtended by the chords AB and AC at the centre of the circle are 60 and 100 degrees respectively. The BOC isa)30 degreesb)50 degreesc)25 degreesd)15 degreese)40 degreesCorrect answer is option 'E'. Can you explain this answer?
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If A, B and C are three consecutive points on the arc of a semi-circle such that the angles subtended by the chords AB and AC at the centre of the circle are 60 and 100 degrees respectively. The BOC isa)30 degreesb)50 degreesc)25 degreesd)15 degreese)40 degreesCorrect answer is option 'E'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If A, B and C are three consecutive points on the arc of a semi-circle such that the angles subtended by the chords AB and AC at the centre of the circle are 60 and 100 degrees respectively. The BOC isa)30 degreesb)50 degreesc)25 degreesd)15 degreese)40 degreesCorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A, B and C are three consecutive points on the arc of a semi-circle such that the angles subtended by the chords AB and AC at the centre of the circle are 60 and 100 degrees respectively. The BOC isa)30 degreesb)50 degreesc)25 degreesd)15 degreese)40 degreesCorrect answer is option 'E'. Can you explain this answer?.
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