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Question
In the following figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the value of ∠ACD + ∠BED.
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Solution
Since, A, C, D and E are four point on a circle, then ACDE is a cyclic quadrilateral.
∠ACD + ∠AED = 180° ...(i) [Sum of opposite angles in a cyclic quadrilateral is 180°]
Now, ∠AEB = 90° ...(ii)
We know that, diameter subtends a right angle to the circle.
On adding equations (i) and (ii), we get
(∠ACD + ∠AED) + ∠AEB = 180° + 90° = 270°
⇒ ∠ACD + ∠BED = 270°
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