Question

The tangent at any point of a circle and the radius through this point are perpendicular to each other.

• A. True
• B. False

Answer 1

The correct option is A

True

Yes, it is true, the tangent at any point of a circle and the radius through this point are perpendicular to each other as shown below.

In the figure above,
$\angle OPA+\angle OPQ={180}^{\circ }$ ........(1) [Linear pair angle]
Also, $\angle OPA=\angle OPQ$ ......(2)
$\therefore$ $\angle OPA+\angle OPQ={180}^{\circ }$
$2\times \angle OPQ={180}^{\circ }$
$\angle OPQ={90}^{\circ }$
Hence, OP is perpendicular to PQ $\Rightarrow$ OP is perpendicular to AB.