In the diagram, A, B, C and D lie on the circumference of a circle with centre O such that AB = AC and EAF is a tangent to the circle at A.

1. Relate angle CAF to an angle inside the triangle using the Alternate Segment Theorem

$\angle ABC = \angle CAF$ (Alternate Segment Theorem)

2. Use the given equal side lengths to relate angles within the triangle

Since $AB = AC$, $\triangle ABC$ is an isosceles triangle.
$\angle BCA = \angle ABC$ (Base angles of isosceles triangle)

3. Conclude the proof by equating the angles

Therefore, $\angle BCA = \angle CAF$. (Shown)

1. Identify equal side lengths to set up a congruence proof for triangles OAB and OAC.

In $\triangle OAB$ and $\triangle OAC$:
$OA = OA$ (Common side)
$OB = OC$ (Radii of the same circle)
$AB = AC$ (Given)

2. Prove the triangles are congruent and conclude the angles are equal.

$\triangle OAB \equiv \triangle OAC$ (SSS congruence test)
Therefore, $\angle OAB = \angle OAC$.
Hence, $OA$ bisects $\angle BAC$.