Question

In figure, AOB is diameter of circle and C,D and E are  any three points on semicircle find ∠ACD + ∠BED

Answer 1

Joing AE and angle in semicircle ACHE is a cyclic quadrilateral opposite angles of cyclic quadrilateral are supplementary

∴ ∠AEB = 90° …(i)

∴ ∠ACD + ∠DEA = 180° …(ii)

Adding equation (i) and (ii)

∠AEB + ∠DEA + ∠ACD = 180° + 90°

∠BED + ∠ACD = 270°

[∵ ∠AEB + ∠DEA = ∠BED]