In Fig.10.15, 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.

Given: AOB is the diameter.


Join AE and ACDE is a cyclic quadrilateral.


ACD + AED = 180° (sum of opposite angles of a cyclic quadrilateral is 180°) ………………(1)


As diameter subtend a right angle to the circle, therefore,


AEB = 90° ………………(2)


Adding equation (1) and (2), we have:


ACD + AED + AEB = 180° + 90°


ACD + BED = 270°


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