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:
Answer & explanation
Correct answer: option 1
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
Therefore, the perimeter of the triangle is 16.6 cm.