Let O be the centre of a circle and AC be its diameter. BD is a chord intersecting AC at E. Point A is joined to B and D. If ∠BOC = 50° and ∠AOD = 110°, then ∠BEC = ?
Show answer & explanation
Correct answer: B
Explanation
Correct Answer is option 2 i.e. 80°
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Concept |
Understanding |
Application |
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Angle subtended by a chord of a circle at centre is double the angle subtended by same chord at circumference of the circle. |
Given ∠BOC = 50°, ∠AOD = 110° |
From the figure: ∠BAC = ∠BOC/2 = 25° Similarly, ∠ABD = ∠AOD/2 = 55° Now in triangle ABE: ∠AEB = 180 – 25 – 55 = 100° Hence, ∠BEC = 180 – 100 = 80° |