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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, - Mathematics

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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. 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

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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 18: Tangents and Intersecting Chords
Exercise 18 (A) | Q: 13.1 | Page no. 275
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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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