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,
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
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