Points and lie consecutively on a circle with centre

MATHEMATICS · Subjective · CBSE · Mathematics · Circles · Circles

Problem

Points

A,\,B,\,C,\,

and

D

lie consecutively on a circle with centre

O

. Chords

AB

and

CD

are equal. The following central angles are known:

\angle AOB = (7y - 8)^{\circ}, \qquad \angle BOC = 50^{\circ}, \qquad \angle COD = (2y + 14)^{\circ}.

(i) Find the value of

y

. (ii) Determine the measures of

\angle AOB,\; \angle BOC,\; \angle COD,

and

\angle DOA