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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.
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.
CBSE | Circles | Class 10 | Exercise 10.2 | Maths | RD Sharma
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.

Given: O and C are the centre of Two circles  touching each other externally at P. PT is its common tangent

From a point T: PT, TR and TQ are the tangents drawn to the circles.

Required to prove: TQ = TR

Proof:

$TR$  and $TP$  are two tangents to the circle with centre $O$ , From $T$

So, $TR=TP$  ….(i)

Similarly, from point $T$

$TQ$  and $TP$  are two tangents to the circle having centre $C$

$TQ=TP$  ….(ii)

From (i) and (ii) ⇒

$TQ=TR$

– Hence proved.

i

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