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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.


  1. Tangent at point P bisects AB.

  2. APB=40

  3. APB=45

  4. APB=10


Solution

The correct option is A

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.
TA and TP are the tangents to the circle from same point T.
 TA = TP     ....(i)
Similarly TP = TB          ....(ii)
From (i) and (ii)
TA = TB
TPT' is the bisector of AB.

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