Two circle touch externally at a point P. From apoint 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

Let the centre of the circles be O and O'.
From T, TQ and TP are two tangents to the circle with centre O
$∴$ TQ = TP ..(i)
Similarly, from T, TR and TP are two tangents to the circle with centre O
$∴$ TR = TP ..(ii)
From (i) and (ii)
TQ = TR

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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

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Two circle touch externally at a point P. From apoint 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.

Let the centre of the circles be O and O'. From T, TQ and TP are two tangents to the circle with centre O ∴ TQ = TP ..(i) Similarly, from T, TR and TP are two tangents to the circle with centre O ∴ TR = TP ..(ii) From (i) and (ii) TQ = TR

Let the centre of the circles be O and O'.
From T, TQ and TP are two tangents to the circle with centre O
$∴$ TQ = TP ..(i)
Similarly, from T, TR and TP are two tangents to the circle with centre O
$∴$ TR = TP ..(ii)
From (i) and (ii)
TQ = TR