Question

6. A circle is touching the side BC of AABC at P and touching AB and AC produded at Q and
R respectively. Prove that AQ = (perimeter of A ABC). If AQ - 5 cm, find the permeter
of A ABC
2
2​

Answer 1

Answer:

Step-by-step explanation:

Lengths of tangents drawn from an external point to a circle are equal.

         ⇒ AQ = AR, BQ = BP, CP = CR.

         Perimeter of ΔABC = AB + BC + CA

                                     = AB + (BP + PC) + (AR – CR)

                                     = (AB + BQ) + (PC) + (AQ – PC) [AQ = AR, BQ = BP, CP = CR]

                                     = AQ + AQ

                                     = 2AQ

          ⇒ AQ = 1/2 (Perimeter of ΔABC)

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