CBSE Class 10 Maths (Standard) 2024 · Paper 30/3/1 · Question 31

When $AB$ is not a diameter, the tangents at $A$ and $B$ meet at an external point $P$ with $PA=PB$, so $△PAB$ is isosceles and $\angle PAB=\angle PBA$: the tangents make equal angles with the chord. When $AB$ is a diameter, both tangents are perpendicular to $AB$, so both angles are $90^{\circ }$. Hence proved.