Question

In the figure TA and TB are tangents drawn from the
external point T. Another tangent PQ touches the circle at R.
Prove that the perimeter of ATPQ = 24T.​

Answer 1

Step-by-step explanation:

perimeter of triangle TPQ=TP+PQ+TQ

=TP+PR+RQ+TQ

PR=AP and RQ=BQ (tangent from external points)

perimeter of triangle TPQ=TP+AP+BQ+TQ

=(TP+PA)+(TQ+QB)

=TA+TB

but TA=TB

perimeter of triangle TPQ=2TA=2TB

Answer 2

Answer:

In triangle TPQ , TP+TQ+PQ

TP+PR+RQ+TQ

PR=AP,RQ=BQ ...tangents from external points

In triangle TPQ, ( TP+AP)+(TQ+BQ)

TA+TB

BUT TA=TB

THERE FORE ATPQ=24T