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In the figure, two circles touch each ot...

In the figure, two circles touch each other at the point C.Prove that the common tangents to the circles at C, bisect the common tangents at P and Q.

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In the given figure, PR and CR are both tangents drawn to the same circle from an external point R
`:." "PR=CR" "…(1)`
Also, QR and CR are both tangent drawn to the same circle from an external point R.
`:." "QR=CR`
From (1) and (2) we get
`PR=QR`
`:.` R is the mid-point of PQ
i.e., the common tangent at C bisects the common tangents at P and Q.
Hence Proved.
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