Two circle touch externally at a point P. From a point T on a tangent at P, tangents TQ and TR are drawn to the circles with points of contact Q and R respectively. Prove that TQ = TR.

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Solution

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From the given figure,
TR, TP are two tangents drawn to bigger circle from an external point T.
we know that,
length of tangents drawn from external point to circle are equal
$∴ T R = T P$ _(i)
Similarly TP, TQ are two tangent drawn to smaller circle from an external point T.
Again we have $T P = T Q$ (ii)
From (i) & (ii), we have $T R = T Q$

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