Question

In the given figure, perimeter of ΔPQR is 20 cm. Find the length of tangent PA.

Answer 1

Given: Perimeter of ΔPQR = 20

i,e, PQ + QR + PR = 20

⇒ PQ + (QC + CR) + PR = 20

⇒ (PQ + QA) + (RB + PR) = 20  ...[∵ QA = QC and RC = RB as tangents from external points Q and R, respectively]

⇒ PA + PB = 20

⇒ PA + PA = 20   ...[∵ PA = PB as tangents from external point P]

⇒ 2PA = 20

⇒ PA = 10 cm