In a circle with centre

MATHEMATICS · Subjective · CBSE · Mathematics · Circles · Circles

Problem

O

, points

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

and

D

lie on the circumference in that order such that chords

AB

and

CD

are equal. A point

P

is any point on the circle on the same side of

AC

as points

B

and

D

. (i) Prove that

\angle AOB = \angle COD

. (ii) If

\angle AOB = 66^{\circ}

, calculate

\angle APB

. (iii) Suppose instead that

\angle APB = 40^{\circ}

. Find the measure (in degrees) of the minor arc

\overset{\frown}{AB}