Question

two circles touch external point P. from a point T on the tangent at P, tangents TQ andTR

Answer 1

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