Points and lie on a circle with and on the same side of chord

MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Circle Theorems

Problem

Points

A, B, C

and

D

lie on a circle with

C

and

D

on the same side of chord

AB

. It is given that

\angle ACB = 51^{\circ}

. (i) Find the value of

\angle ADB

. (ii) If chord

BC

is joined and

\angle BAC = 38^{\circ}

, determine

\angle BDC

. (iii) Write all the angle equalities you have used in parts (i) and (ii), stating clearly the chord responsible for each equality.