In the adjoining figure, is a chord parallel to diameter of the circle with center If calculate

Question

Philoid · Accepted Answer

∠CAD and ∠CBD are in the segment BD.

∴ ∠CAD = ∠CBD [Angles in the same segment of a circle]

∠CAD = 60°

In triangle ACD,

∠CAD + ∠ADC + ∠ACD = 180°[Sum of angles of triangle]

⇒ 60° + 90° + ∠ACD = 180°

⇒ 150° + ∠ACD = 180°

⇒ ∠ACD = 30°

∴ ∠CDE = ∠ACD = 30°[Alternate angles]