Question

The perpendicular of the point of contact to the tangent to a circle passes through the center

• A. True
• B. False

Answer 1

The correct option is A True

Given : Let us assume a circle with centre O & AB be the tangent intersecting circle at point P.

Proof :

We know that,

Tangent of circle is perpendicular to radius at point of contact.

Hence, $OP\perp AB$

So, $\angle OPB={90}^o$ ......(1)

Now, let's assume some point X, such that $XP\perp AB$.

Hence, $\angle XPB={90}^o$ .....(2)

From 1 and 2,

$\angle OPB=\angle XPB={90}^o$ which is possible only if line XP passes through O.

Hence, perpendicular to tangent passes through centre.