CBSE Class 10 Maths (Standard) 2024 · Paper 30(B)/S · Question 22(a)

Let tangents $PQ$ and $RS$ touch the circle at $A$ and $B$, with $PQ\parallel RS$. Since a tangent is perpendicular to the radius at the point of contact, $\angle PAO=\angle RBO=90^{\circ }$. Drawing $OC\parallel PQ$ through $O$, co-interior angles give $\angle AOC=90^{\circ }$ and $\angle BOC=90^{\circ }$, so $\angle AOC+\angle BOC=180^{\circ }$ and $A$, $O$, $B$ lie on one straight line. Hence $AB$ passes through the centre $O$. Hence proved.