Question

In the given figure, two circles touch each other externally at point, P. AB is the direct common tangent of these circles. Select the statements that are true.

• A. $\angle APB={40}^{\circ }$
• B. Tangent at point P bisects AB.
• C. $\angle APB={45}^{\circ }$
• D. $\angle APB={10}^{\circ }$

Answer 1

The correct option is B

Tangent at point P bisects AB.

Given - Two circles with centre O and O' touches each other at P externally. AB is the direct common tangent touching the circles at A and B respectively.

AP, BP are joined, TPT' is the common tangent to the circles.
By Theorem - Tangents drawn from an external point to the circle are equal in lengths.
$\because$ TA and TP are the tangents to the circle from same point T.
$\therefore$ TA = TP ....(i)
Similarly TP = TB ....(ii)
From (i) and (ii)
TA = TB
$\therefore$ TPT' is the bisector of AB.