#### Question

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

tangent at point P bisects AB,

#### Solution

Draw TPT' as common tangent to the circles.

i) TA and TP are the tangents to the circle with centre O.

Therefore, TA = TP ………(i)

Similarly, TP = TB ………..(ii)

From (i) and (ii)

TA = TB

Therefore, TPT' is the bisector of AB

Is there an error in this question or solution?

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In the Given Figure, Two Circles Touch Each Other Externally at Point P. Ab is the Direct Common Tangent of These Circles. Prove that Tangent at Point P Bisects Ab, Concept: Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers.

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