Two circles touch externally at a point P. From a point T on the 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

We know that the lengths of tangents drawn from an external point to a circle are equal.

In the given figure, TQ and TP are tangents drawn to the same circle from an external point T.

∴ TQ = TP .....(1)

Also, TP and TR are tangents drawn to the same circle from an external point T.

∴ TP = TR .....(2)

From (1) and (2), we get

TQ = TR

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Similar questions

In the given figure, there are two circles with the centres O and O' touching each other internally at P. Tangents TQ and TP are drawn to the larger circle and tangents TP and TR are drawn to the smaller circle . Find TQ : TR

Q. Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that

∠ P T Q = 2 ∠ O P Q

From an external point $T,$ two tangents $T P$ and $T Q$ are drawn to a circle having it's center at O. Prove that $∠ P T Q = 2 ∠ O P Q$

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