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Question -

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.



Answer -

Given : Two circles with centres O and C touch each other externally at P. PT is its common tangent
From a point T on PT, TR and TQ are the tangents drawn to the circles
 
To prove : TQ = TR
Proof : From T, TR and TP are two tangents to the circle with centre O
TR = TP ….(i)
Similarly, from T,
TQ and TP are two tangents to the circle with centre C
TQ = TP ….(ii)
From (i) and (ii)
TQ = TR
Hence proved.

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