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Question

In the given figure, a circle touches the side BC of ΔABC at P. AB and AC are two tangents drawn from a point A outside the circle. If AQ = 15 cm, find the perimeter of ΔABC.


A
60 cm
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B
40 cm
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C
30 cm
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D
35 cm
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Solution

The correct option is C 30 cm

From the figure,
AQ=AR
[Tangents drawn from a point outside the circle are equal in length]

AQ=AC+CR(AR=AC+CR)

CR=CP
[Tangents drawn from a point outside the circle are equal in length]

AQ=AC+CP...(i)

Also, AQ=AB+BQ

But, BQ=BP
[Tangents drawn from a point outside the circle are equal in length]

AQ=AB+BP...(ii)

Adding equations (i) and (ii),

2AQ=AC+CP+BP+AB

2AQ=Perimeter of ΔABC

Perimeter of ΔABC=2×15=30 cm


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