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