Multiple choice

A circle is inscribed in a triangle ABC. It touches the sides AB, BC and AC at the points R, P and Q, respectively. If AQ = 4.5 cm, PC = 5.5 cm and BR = 6 cm, then the perimeter of the triangle ABC is

  1. 30.5 cm

  2. 28 cm

  3. 32 cm

  4. 26.5 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Tangents from a point to a circle are equal. AQ = AR = 4.5. PC = PQ = 5.5. BR = BP = 6. Sides are AB = 4.5+6 = 10.5, BC = 6+5.5 = 11.5, AC = 4.5+5.5 = 10. Perimeter = 10.5 + 11.5 + 10 = 32.

AI explanation

The tangent segments to a circle from an external point are equal in length, meaning AQ = AR, BR = BP, and CP = CQ. The side lengths of the triangle are AB = 6 + 4.5 = 10.5 cm, BC = 6 + 5.5 = 11.5 cm, and AC = 4.5 + 5.5 = 10 cm. Adding these three sides gives the perimeter as 10.5 + 11.5 + 10 = 32 cm.

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