In a circle, chord subtends two inscribed angles at points and on the same side of…

MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles

Problem

In a circle, chord

MN

subtends two inscribed angles at points

P

and

Q

on the same side of

MN

. (i) Given

\angle MPN = (4x + 15)^\circ

and

\angle MQN = (7x - 9)^\circ

, determine the value of

x

and hence the measure of each angle. (ii) Using your result from part (i), find the size of the central angle

\angle MON

, where

O

is the centre of the circle.