Multiple choice

A circle is inscribed in (\triangle ABC), touching AB at P, BC at Q and AC at R. If AR = 5 cm , RC = 6 and AB = 12 cm, then the perimeter of (\triangle ABC) is?

  1. 40

  2. 32

  3. 37

  4. 36
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a circle inscribed in a triangle, tangents from a point to a circle are equal. So AR = 5, so RP = 5. BP = AB - AP = 12 - 5 = 7, so BQ = 7. RC = 6, so CQ = 6. Perimeter = AB + BC + CA = 12 + (BQ + CQ) + (AR + RC) = 12 + 13 + 11 = 36.

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