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Two circles intersect each other at the points A and B. A straight line parallel to AB intersects the circles at C, D, E and F. If CD = 4.5 cm, then the measure of EF is (SSC CHSL 2014)
- a)1.50 cm
- b)2.25 cm
- c)4.50 cm
- d)9.00 cm
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Two circles intersect each other at the points A and B. A straight lin...
As we see, DE is the chord of the circle with center ‘O’
then, line OO' ⊥ bisect DE
∴ DM = ME ...(i)
Again, CF is the chord of the circle with center O'.
Again line OO' ⊥ bisect CF
∴ CM = MF
⇒ CD + DM = ME + EF
4.5 + DM = DM + EF {from (i)}
∴ EF = 4.5 cm
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Community Answer
Two circles intersect each other at the points A and B. A straight lin...
To find the measure of EF, we need to make use of the properties of intersecting circles and parallel lines.
Let's break down the problem step by step:
1. Drawing the diagram:
Draw two circles intersecting each other at points A and B. Then draw a straight line parallel to AB. Label the points of intersection with the circles as C, D, E, and F.
2. Identifying the given information:
The problem states that CD = 4.5 cm. This is the length of the line segment CD.
3. Understanding the properties of intersecting circles:
When two circles intersect each other, the angle formed by any two points of intersection and the center of the circles is equal.
4. Identifying the angles in the diagram:
From the property mentioned above, we can observe that angles CAD and DAE are equal, and angles CBF and FBE are equal. Similarly, angles CDB and DEA are equal, and angles CFB and EBF are equal.
5. Using the property of parallel lines:
Since the line EF is parallel to AB, the angles CDE and EFB are equal, as they are corresponding angles.
6. Setting up the equation:
Let's assume the measure of EF to be x cm. From the information given, we can set up the following equation:
4.5 (CD) + x (EF) = 2π (circumference of the circle)
7. Solving the equation:
Since the circles intersect at points A and B, the circumference of each circle is equal to the perimeter of the circle passing through points A, B, C, D, E, and F. The perimeter of this circle is 2π (EF + CD). Substituting this into the equation, we get:
4.5 + x = 2π (EF + 4.5)
8. Simplifying the equation:
Since we are only interested in finding the measure of EF, we can solve for x:
x = 2π (EF + 4.5) - 4.5
x = 2π EF + 9π - 4.5
9. Finding the value of EF:
Now, we substitute the given options into the equation and check which one satisfies it.
a) 1.50 cm: x = 2π(1.50) + 9π - 4.5 = 3π + 9π - 4.5 = 12π - 4.5
b) 2.25 cm: x = 2π(2.25) + 9π - 4.5 = 4.5π + 9π - 4.5 = 13.5π - 4.5
c) 4.50 cm: x = 2π(4.50) + 9π - 4.5 = 9π + 9π - 4.5 = 18π - 4.5
d) 9.00 cm: x = 2π(9.00) + 9π - 4.5 = 18π + 9π - 4.5 = 27π - 4.5
10. Comparing the options:
Since we are looking for the measure of EF, we need to find the option that satisfies the equation. Comparing the values
Let's break down the problem step by step:
1. Drawing the diagram:
Draw two circles intersecting each other at points A and B. Then draw a straight line parallel to AB. Label the points of intersection with the circles as C, D, E, and F.
2. Identifying the given information:
The problem states that CD = 4.5 cm. This is the length of the line segment CD.
3. Understanding the properties of intersecting circles:
When two circles intersect each other, the angle formed by any two points of intersection and the center of the circles is equal.
4. Identifying the angles in the diagram:
From the property mentioned above, we can observe that angles CAD and DAE are equal, and angles CBF and FBE are equal. Similarly, angles CDB and DEA are equal, and angles CFB and EBF are equal.
5. Using the property of parallel lines:
Since the line EF is parallel to AB, the angles CDE and EFB are equal, as they are corresponding angles.
6. Setting up the equation:
Let's assume the measure of EF to be x cm. From the information given, we can set up the following equation:
4.5 (CD) + x (EF) = 2π (circumference of the circle)
7. Solving the equation:
Since the circles intersect at points A and B, the circumference of each circle is equal to the perimeter of the circle passing through points A, B, C, D, E, and F. The perimeter of this circle is 2π (EF + CD). Substituting this into the equation, we get:
4.5 + x = 2π (EF + 4.5)
8. Simplifying the equation:
Since we are only interested in finding the measure of EF, we can solve for x:
x = 2π (EF + 4.5) - 4.5
x = 2π EF + 9π - 4.5
9. Finding the value of EF:
Now, we substitute the given options into the equation and check which one satisfies it.
a) 1.50 cm: x = 2π(1.50) + 9π - 4.5 = 3π + 9π - 4.5 = 12π - 4.5
b) 2.25 cm: x = 2π(2.25) + 9π - 4.5 = 4.5π + 9π - 4.5 = 13.5π - 4.5
c) 4.50 cm: x = 2π(4.50) + 9π - 4.5 = 9π + 9π - 4.5 = 18π - 4.5
d) 9.00 cm: x = 2π(9.00) + 9π - 4.5 = 18π + 9π - 4.5 = 27π - 4.5
10. Comparing the options:
Since we are looking for the measure of EF, we need to find the option that satisfies the equation. Comparing the values
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Two circles intersect each other at the points A and B. A straight line parallel to AB intersects the circles at C, D, E and F. If CD = 4.5 cm, then the measure of EF is (SSC CHSL 2014)a)1.50 cmb)2.25 cmc)4.50 cmd)9.00 cmCorrect answer is option 'C'. Can you explain this answer?
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Two circles intersect each other at the points A and B. A straight line parallel to AB intersects the circles at C, D, E and F. If CD = 4.5 cm, then the measure of EF is (SSC CHSL 2014)a)1.50 cmb)2.25 cmc)4.50 cmd)9.00 cmCorrect answer is option 'C'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Two circles intersect each other at the points A and B. A straight line parallel to AB intersects the circles at C, D, E and F. If CD = 4.5 cm, then the measure of EF is (SSC CHSL 2014)a)1.50 cmb)2.25 cmc)4.50 cmd)9.00 cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two circles intersect each other at the points A and B. A straight line parallel to AB intersects the circles at C, D, E and F. If CD = 4.5 cm, then the measure of EF is (SSC CHSL 2014)a)1.50 cmb)2.25 cmc)4.50 cmd)9.00 cmCorrect answer is option 'C'. Can you explain this answer?.
Two circles intersect each other at the points A and B. A straight line parallel to AB intersects the circles at C, D, E and F. If CD = 4.5 cm, then the measure of EF is (SSC CHSL 2014)a)1.50 cmb)2.25 cmc)4.50 cmd)9.00 cmCorrect answer is option 'C'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Two circles intersect each other at the points A and B. A straight line parallel to AB intersects the circles at C, D, E and F. If CD = 4.5 cm, then the measure of EF is (SSC CHSL 2014)a)1.50 cmb)2.25 cmc)4.50 cmd)9.00 cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two circles intersect each other at the points A and B. A straight line parallel to AB intersects the circles at C, D, E and F. If CD = 4.5 cm, then the measure of EF is (SSC CHSL 2014)a)1.50 cmb)2.25 cmc)4.50 cmd)9.00 cmCorrect answer is option 'C'. Can you explain this answer?.
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Two circles intersect each other at the points A and B. A straight line parallel to AB intersects the circles at C, D, E and F. If CD = 4.5 cm, then the measure of EF is (SSC CHSL 2014)a)1.50 cmb)2.25 cmc)4.50 cmd)9.00 cmCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Two circles intersect each other at the points A and B. A straight line parallel to AB intersects the circles at C, D, E and F. If CD = 4.5 cm, then the measure of EF is (SSC CHSL 2014)a)1.50 cmb)2.25 cmc)4.50 cmd)9.00 cmCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Two circles intersect each other at the points A and B. A straight line parallel to AB intersects the circles at C, D, E and F. If CD = 4.5 cm, then the measure of EF is (SSC CHSL 2014)a)1.50 cmb)2.25 cmc)4.50 cmd)9.00 cmCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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