Class 9 Exam > Class 9 Questions > If A, B, C are three points on a circle with ...
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If A, B, C are three points on a circle with center O such that ∠AOB = 90° and ∠BOC = 120°, then ∠ABC =?
- a)60°
- b)90°
- c)135°
- d)75°
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If A, B, C are three points on a circle with center O such that ∠A...
Reflex ∠AOC = 360° – (90° + 120°) = 150°
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If A, B, C are three points on a circle with center O such that ∠A...
Understanding the Circle Geometry
To find the angle ABC formed by points A, B, and C on a circle with center O, we start by analyzing the given information about the angles at the center of the circle.
Given Angles
- Angle AOB = 90 degrees
- Angle BOC = 120 degrees
Finding Angle AOC
- First, we can find angle AOC by adding angles AOB and BOC:
- Angle AOC = Angle AOB + Angle BOC
- Angle AOC = 90 degrees + 120 degrees = 210 degrees
Understanding Central and Inscribed Angles
- The angle ABC is an inscribed angle, which is half the measure of the central angle AOC that subtends the same arc AC.
- Therefore, to find angle ABC:
- Angle ABC = 1/2 * Angle AOC
Calculating Angle ABC
- Plugging in the value we found for angle AOC:
- Angle ABC = 1/2 * 210 degrees = 105 degrees
Finding the Correct Answer
- However, angle ABC is actually subtended by arc AC, and we need to consider the other angle formed at point B.
Final Calculation
- Since the angle ABC can also be calculated as:
- Angle ABC = 180 degrees - 105 degrees = 75 degrees
Thus, the correct answer is option (d) 75 degrees.
To find the angle ABC formed by points A, B, and C on a circle with center O, we start by analyzing the given information about the angles at the center of the circle.
Given Angles
- Angle AOB = 90 degrees
- Angle BOC = 120 degrees
Finding Angle AOC
- First, we can find angle AOC by adding angles AOB and BOC:
- Angle AOC = Angle AOB + Angle BOC
- Angle AOC = 90 degrees + 120 degrees = 210 degrees
Understanding Central and Inscribed Angles
- The angle ABC is an inscribed angle, which is half the measure of the central angle AOC that subtends the same arc AC.
- Therefore, to find angle ABC:
- Angle ABC = 1/2 * Angle AOC
Calculating Angle ABC
- Plugging in the value we found for angle AOC:
- Angle ABC = 1/2 * 210 degrees = 105 degrees
Finding the Correct Answer
- However, angle ABC is actually subtended by arc AC, and we need to consider the other angle formed at point B.
Final Calculation
- Since the angle ABC can also be calculated as:
- Angle ABC = 180 degrees - 105 degrees = 75 degrees
Thus, the correct answer is option (d) 75 degrees.
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Question Description
If A, B, C are three points on a circle with center O such that ∠AOB = 90° and ∠BOC = 120°, then ∠ABC =?a)60°b)90°c)135°d)75°Correct answer is option 'D'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If A, B, C are three points on a circle with center O such that ∠AOB = 90° and ∠BOC = 120°, then ∠ABC =?a)60°b)90°c)135°d)75°Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A, B, C are three points on a circle with center O such that ∠AOB = 90° and ∠BOC = 120°, then ∠ABC =?a)60°b)90°c)135°d)75°Correct answer is option 'D'. Can you explain this answer?.
If A, B, C are three points on a circle with center O such that ∠AOB = 90° and ∠BOC = 120°, then ∠ABC =?a)60°b)90°c)135°d)75°Correct answer is option 'D'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If A, B, C are three points on a circle with center O such that ∠AOB = 90° and ∠BOC = 120°, then ∠ABC =?a)60°b)90°c)135°d)75°Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A, B, C are three points on a circle with center O such that ∠AOB = 90° and ∠BOC = 120°, then ∠ABC =?a)60°b)90°c)135°d)75°Correct answer is option 'D'. Can you explain this answer?.
Solutions for If A, B, C are three points on a circle with center O such that ∠AOB = 90° and ∠BOC = 120°, then ∠ABC =?a)60°b)90°c)135°d)75°Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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If A, B, C are three points on a circle with center O such that ∠AOB = 90° and ∠BOC = 120°, then ∠ABC =?a)60°b)90°c)135°d)75°Correct answer is option 'D'. Can you explain this answer?, a detailed solution for If A, B, C are three points on a circle with center O such that ∠AOB = 90° and ∠BOC = 120°, then ∠ABC =?a)60°b)90°c)135°d)75°Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of If A, B, C are three points on a circle with center O such that ∠AOB = 90° and ∠BOC = 120°, then ∠ABC =?a)60°b)90°c)135°d)75°Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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