Question

# In the figure, a circle touches the side BC of $$\triangle$$ ABC at P and sides AB and AC produced at Q and R respectively. What is the perimeter of $$\triangle$$ ABC if AQ = 5 cm?

A
10cm
B
3cm
C
17cm
D
7cm

Solution

## The correct option is A $$10 cm$$Using the property that lenghts of tangents drawn from an external point to circle is same.$$AQ=AR=5cm$$Let $$CR=CP=x$$ and $$BP=BQ=y$$Also, $$AC= AR- CR=$$ $$5-x$$ and AB=AQ-BQ= $$5-y$$Perimeter of $$\Delta ABC= AC+BC+AB$$$$\Rightarrow (5-x)+(5-y)+x+y$$$$\Rightarrow 10 cm$$Maths

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