Multiple choice

A circle is inscribed in a triangle ABC. It touches sides AB, BC and AC at the points P, Q and R respectively. If BP = 6.5 cm, CQ = 4.5 cm and AR = 5.5 cm, then the perimeter (in cm) of the triangle ABC is?

  1. $16.5$
  2. $22$
  3. $33$
  4. $66$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a circle inscribed in a triangle, tangents from a vertex to the incircle are equal. From B: BP = BQ = 6.5. From C: CQ = CP = 4.5. From A: AR = AP = 5.5. Perimeter = AB + BC + AC = (AP + BP) + (BQ + CQ) + (CP + AR) = (5.5 + 6.5) + (6.5 + 4.5) + (4.5 + 5.5) = 33cm. Option C is correct.

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