A, B, R and P are four points on a circle with centre O - Edexcel - GCSE Maths - Question 21 - 2018 - Paper 2

In triangle OAB, since O is the center of the circle, the angles at the circumference subtended by the same arc are equal. Hence:

$ext{angle } AOB = 2 imes ext{angle } ACB$

Following this, by the properties of cyclic quadrilaterals, we can express angle CRB similarly.

From the properties of the circle, we can say that:

$ext{angle } ACB = ext{angle } ABC$

This equality holds since both angles subtend the same arc AB in the circle.

By combining the earlier results, we can deduce:

$ext{angle } CAB + ext{angle } ABC = 180°$

Therefore, angle CAB equals angle ABC, which proves the statement required.