CBSE Class 10 Maths (Basic) 2025 · Paper 430/2/1 · Question 23

Let $O$ be the centre, $\ell$ the tangent at $A$ and $OA$ the radius. Every point $B$ of $\ell$ other than $A$ lies outside the circle, so $OB>OA$. Thus $OA$ is the shortest distance from $O$ to $\ell$, and the shortest distance from a point to a line is the perpendicular one. Hence $OA\perp \ell$. Hence proved.