Question

AB is the diameter of the circle with centre O. OD is parallel to BC and $\angle$ AOD = ${60}^o$, Calculate the numerical values of :

(i) $\angle$ ABD ,

(ii) $\angle$ DBC,

(iii) $\angle$ ADC.

Answer 1

Join B and D as shown in the diagram.

(i) (angle subtended by an chord on the center is double that subtended by the same chord on the circumference)

(ii) (angle in semi circle)

Since is equilateral

Since

(alternate angles)

(ii)

( is a cyclic quadrilateral)