Question

A circle touches the side BC of ∆ ABC at P, AB and AC produced at Q and R respectively, then find that ___AR = perimeter of ∆ ABC

• A. 4
• B. 3
• C. 2
• D. 1

Answer 1

The correct option is C

2

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We know that length of the two tangents from an exterior point to a circle are equal.

AQ = AR as well as BP = BQ and CP = CR ------(i)

Now, perimeter of ∆ ABC = AB + BC + AC = AB + (BP + PC) + AC

= (AB + BQ) + (CR + AC) --------(i)

= AQ + AR --------(ii)

But, AR = AQ perimeter of ∆ ABC = 2 AQ or 2 AR