Mathematics

Problem

Points

A

and

B

are fixed in a plane. Two points

C

and

D

are chosen on the same side of

AB

such that

\angle ACB = \angle ADB = 55^\circ

. It is further given that

\angle ABC = 42^\circ

. a. (i) Prove that the four points

A,\,B,\,C

and

D

lie on one circle. b. (ii) Hence, calculate the measure of

\angle ADC