A, B, R and P are four points on a circle with centre O - Edexcel - GCSE Maths - Question 1 - 2018 - Paper 2

Next, we can further analyze triangle AOB. Lines AOB and ARC are also linear pairs since A, O, and R are collinear points. By properties of inscribed angles:

$\angle AOB = 2 \times \angle CAB$

Similarly, the same property applies to angles subtended at both arcs such that:

$\angle RAB = 2 \times \angle ABC$

Thus,

$\angle AOB + \angle ARC = 180^{\circ}$

Finally, since both angles are equal and supplementary:

$\angle CAB + \angle ABC = 180^{\circ}$

we can conclude that:

$\angle CAB = \angle ABC$

Therefore, we have completed the proof, corroborating the initial statement that angle CAB equals angle ABC.