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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 $$\triangle ABC$$.
507259_81020fc4fafa4286a7fb25f1b0fa4161.png


A
6 cm
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B
10 cm
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C
12 cm
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D
15 cm
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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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