Question

Solve this step by step​

Answer 1

Since the arcs AC and BD are equal,

⟨ABC = ⟨BAD ...(1)

because the arcs of equal length subtend equal angles on the circle, or at the center of the circle.

But, in ∆ABD and ∆BED,

⟨ADB = ⟨BED = 90°

(⟨ADB is the angle subtended by the diameter on the circle; DE is perpendicular to AB.)

⟨DBA = ⟨DBE (common angle)

Therefore,

⟨BDE = ⟨BAD ...(2)

From (1) and (2),

⟨ABC = ⟨BDE

Hence Proved!