Question : A circle is inscribed in a triangle ABC. It touches sides AB, BC and AC at points R, P and Q, respectively. If AQ = 3.5 cm, PC = 4.5 cm and BR = 7 cm, then the perimeter (in cm) of the triangle $\triangle \mathrm{ABC}$ is:
Option 1: 30
Option 2: 15
Option 3: 28
Option 4: 45
Correct Answer: 30
Solution :
AQ = 3.5 cm, PC = 4.5 cm and BR = 7 cm
AQ and AR are two tangents on the circle from point A.
⇒ AQ = AR = 3.5 cm
BP and BR are two tangents on the circle from point B.
⇒ BP = BR = 7 cm
CP and CQ are two tangents on the circle from point C.
⇒ CP = CQ = 4.5 cm
Perimeter of $\triangle$ ABC
= AB + BC + CA
= AR + RB + BP + PC + CQ + QA
= 3.5 + 7 + 7 + 4.5 + 4.5 + 3.5
= 30 cm
Hence, the correct answer is 30.
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