A circle is inscribed in a triangle ABC. It touches sides AB, BC and AC at points R, P and Q, respectively. If AQ = 6.5 cm, PC =7.5 cm and BR = 9 cm, then the perimeter (in cm) of the triangle ABC will be:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 46.
Explanation:
According to the given question,
AR and AQ are the tangents from A to cirlce.
Similarily, BR and BP; CQ and CP are tangents
The tangents from a same poimt to the circle are equal,
⇒ AR = AQ = 6.5 cm; BR = BP = 9 cm; CP = CQ = 7.5 cm
Now, AB = AR + BR = 6.5 + 9 = 15.5 cm
BC = BP + CP = 9 + 7.5 = 16.5 cm
AC = AQ + CQ = 6.5 + 7.5 = 14 cm
So, perimeter = AB + BC + AC = 15.5 + 16.5 + 14 = 46 cm
Hence the required answer is 46 cm.