Question

# In the given figure, a circle touches the side $$BC$$ of $$\triangle ABC$$ at $$P$$ and touches $$AB$$ and $$AC$$ produced at $$Q$$ and $$R$$ respectively. If $$AQ = 5\ cm$$, find the perimeter of $$\triangle ABC$$.

A
6 cm
B
10 cm
C
12 cm
D
15 cm

Solution

## The correct option is B $$10\ cm$$Given, $$AQ=5\;cm$$$$AR=AQ$$ (tangent of point A)also $$CR=CP \quad (1) \\ BQ=BP \quad (2)$$Adding $$(1)$$ and $$(2)$$$$CP+BP=CR+BQ \\ BC=CR+BQ \quad (3)$$Perimeter of $$\triangle ABC$$$$=AC+BC+AB \\ =AC+CR+AB+BQ \; \;from\;(3) \\ =AR+AQ \\ =10\;cm$$Mathematics

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