Question

In the given figure, AD is a diameter. O is the centre of the circle. AD is parallel to BC and ∠CBD = 32°. 

Find: ∠BED  

Answer 1

In Δ OAB ,

OA = OB   ...(Radii of the same circle° )

⇒ ∠ OAB = ∠ OBA = x (say)

⇒ ∠ OAB + ∠ OBA + ∠ AOB = 180°

⇒ x + x + 64° = 180°

⇒ 2x = 180 ° - 64 °

⇒ 2x = 116°

⇒ x =  58°

⇒ ∠ OAB = 58°

i.e. ∠ DAB = 58°

⇒ ∠ DAB = ∠BED = 58°   ....(Angles inscribed in the same arc are equal)