Question

a circle touches the side BC of an triangle ABC at P and AC produced at Q and R respectively. If AQ =6 cm,Find the perimeter of triangle ABC​

Answer 1

Tangents drawn from an external point to the circle are equal.

BP = BQ ….(1)

CP = CR ….(2)

AQ = AR ….(3)

Now, AQ = AR

⇒ AB + BQ = AC + CR

⇒ AB + BP = AC + CP (Using (1) and (2))

Perimeter of ∆ABC = AB + BC + CA

= AB + (BP + PC) + AC

= (AB + BP) + (PC + AC)

= 2(AB + BP) ( AB + BP = AC + CP)

= 2(AB + BQ) (Using (1))

= 2AQ