In a circle, chord is drawn. Points and lie on the circumference on the same side of…

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

Problem

In a circle, chord

AC

is drawn. Points

B

and

D

lie on the circumference on the same side of

AC

. The angles

\angle ABC

and

\angle ADC

are given by

2y + 10^{\circ}

and

7y - 50^{\circ}

respectively. (i) State the relationship between

\angle ABC

and

\angle ADC

, giving a suitable reason. (ii) Find the value of

y

and hence the numerical value of each of these two angles. (iii) If

O

is the centre of the circle, determine the measure of the central angle

\angle AOC

that subtends the same arc

AC