Assertion (A) : TA and TB are two tangents drawn from an external point $T$ to a circle with centre

Question

Assertion (A) : TA and TB are two tangents drawn from an external point $T$ to a circle with centre ' $O$ '. If $\angle T B A=75^{\circ}$ then $\angle A B O=25^{\circ}$.\Reason (R) : The tangent drawn at any point of a circle is perpendicular to the radius through the point of contact.\

Professor PC Thomas Classes · Answer

(d) : $\angle \mathrm{OBT}=90^{\circ}$ [Tangent drawn at any point of a circle is perpendicular to the radius through the point of contact]\ Also, $\angle T B A=75^{\circ}$ (Given)\ Now, $\angle \mathrm{OBT}=\angle \mathrm{ABO}+\angle \mathrm{TBA}$\ $\Rightarrow 90^{\circ}=\angle A B O+75^{\circ} \Rightarrow \angle A B O=15^{\circ}$\ ⇒ Assertion is false, but reason is true.\