Draw a circle with centre

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

Problem

O

. Three points

A, B

and

C

lie in that order on the circumference. The measures of the central angles are:

\angle AOB = 2x^{\circ}

\angle BOC = (x + 20)^{\circ}

\angle COA = (3x - 10)^{\circ}

. (i) Write an equation in

x

using the fact that the sum of the three central angles is

360^{\circ}

. (ii) Solve the equation to find the value of

x

. (iii) Hence determine the measures of arcs

AB

BC

and

CA