Question

In the given figure, M is the centre of the circle. Chords AB and CD are perpendiculat to each other.

If $\angle$ MAD = x and $\angle$ BAC = y :

(i) express $\angle$ AMD in terms of x.

(ii) express $\angle$ ABD in terms of y.

(iii) prove that : x = y.

Answer 1

In the figure, M is the centre of the circle.

Chords AB and CD are perpendicular to each other at L.

(Angle in the same segment)

(Angle at the centre is double the angle at the circumference subtended by the same chord)

Hence Proved.