A circle is inscribed in a triangle ABC. It touches side AB, BC and AC at points R, P and Q, respectively. If AQ = 2.6 cm, PC = 2.7 cm and BR = 3 cm, then the perimeter (in cm) of the triangle △ABC is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e 16.6.
The lengths of two tangents drawn on a circle from an outside point are the same.
AQ and AR are two tangents on the circle from point A
⇒ AQ = AR = 2.6 cm
BP and BR are two tangents on the circle from point B
⇒ BR = BP = 3 cm
CP and CQ are two tangents on the circle from point C
⇒ CP = CQ = 2.7 cm
The perimeter of the triangle is AB + BC + CA = AR + RB + BP + PC + CQ + QA
⇒ 2.6 + 3 + 3 + 2.7 + 2.7 + 2.6 = 16.6
The perimeter of the triangle is 16.6 cm.