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In the given figure two circles touch ea...

In the given figure two circles touch each other at the point C. Prove that the common tangent 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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