Q15 of 52 Page 10

In Fig. 2, two circles touch each other at the point C. Prove that the common tangent to the circles at C, bisects the common tangent P and Q. (CBSE 2013)

From the figure,

PR = RC [Tangents from an external point to the same circle are equal]


RQ = RC [Tangents from an external point to the same circle are equal]


⸫ R is the midpoint of P and Q.


Hence, the common tangent at C bisects P and Q.

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