Points and lie on a circle with centre such that chords and are equal

MATHEMATICS · Single correct · CBSE · Mathematics · Circles · Circles

Problem

Points

A, B,

and

C

lie on a circle with centre

O

such that chords

AB

and

BC

are equal. If

\angle AOB = (3x - 15)^\circ

and

\angle BOC = (x + 45)^\circ

, then

x

equals which value, and what is the measure of

\angle AOC

? (a)

x = 30^{\circ},\; \angle AOC = 210^{\circ}

(b)

x = 15^{\circ},\; \angle AOC = 90^{\circ}

(c)

x = 30^{\circ},\; \angle AOC = 150^{\circ}

(d)

x = 45^{\circ},\; \angle AOC = 150^{\circ}