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What will be the measure of ∠BAE in the given figure with centre O, if AB and AE are tangents and CD is the diameter of the semicircle?
- a)60°
- b)80°
- c)100°
- d)120°
Correct answer is option 'A'. Can you explain this answer?
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What will be the measure of ∠BAE in the given figure with centre O...
In △BEO,
∠BEO = ∠EBO = 30° [Because OE = OB]
∠BEO + ∠EBO + ∠EOB = 180°
⇒ 30° + 30° + ∠EOB = 180°
⇒ ∠EOB = 180° - 60°
⇒ ∠EOB = 120°
Also, ∠ABO = ∠AEO = 90° [Tangent is perpendicular to the radius of circle]
So, in quadrilateral ABOE,
∠ABO + ∠AEO + ∠EOB + ∠BAE = 360°
⇒ 90° + 90° + 120° + ∠BAE = 360°
⇒ ∠BAE = 360° - [90° + 90° + 120°]
⇒ ∠BAE = 360° - 300°
⇒ ∠BAE = 60°
∠BEO = ∠EBO = 30° [Because OE = OB]
∠BEO + ∠EBO + ∠EOB = 180°
⇒ 30° + 30° + ∠EOB = 180°
⇒ ∠EOB = 180° - 60°
⇒ ∠EOB = 120°
Also, ∠ABO = ∠AEO = 90° [Tangent is perpendicular to the radius of circle]
So, in quadrilateral ABOE,
∠ABO + ∠AEO + ∠EOB + ∠BAE = 360°
⇒ 90° + 90° + 120° + ∠BAE = 360°
⇒ ∠BAE = 360° - [90° + 90° + 120°]
⇒ ∠BAE = 360° - 300°
⇒ ∠BAE = 60°
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What will be the measure of ∠BAE in the given figure with centre O, if AB and AE are tangents and CD is the diameter of the semicircle?a)60°b)80°c)100°d)120°Correct answer is option 'A'. Can you explain this answer?
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What will be the measure of ∠BAE in the given figure with centre O, if AB and AE are tangents and CD is the diameter of the semicircle?a)60°b)80°c)100°d)120°Correct answer is option 'A'. 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 What will be the measure of ∠BAE in the given figure with centre O, if AB and AE are tangents and CD is the diameter of the semicircle?a)60°b)80°c)100°d)120°Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the measure of ∠BAE in the given figure with centre O, if AB and AE are tangents and CD is the diameter of the semicircle?a)60°b)80°c)100°d)120°Correct answer is option 'A'. Can you explain this answer?.
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