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Number of Tangents Drawn from a Given Point

In fig., a ci...

Question

In fig., a circle touches the side BC of $Δ A B C$ at P and touches AS and AC produced at Q and R respectively. If AQ = 5 cm, find the perimeter of $Δ A B C$ .

11 cm

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10 cm

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6 cm

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7 cm

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Solution

The correct option is B 10 cm
$A Q = 5$ cm $= A R$ (tangents drawn from the same external point are equal in length)
Also, $B P = B Q$ and $C P = C R$
Perimeter of $△ A B C = A B + B C + A C = A B + (B P + P C) + (A R - C R) = (A B + B P) + P C + (A R - C R) = (A B + B P) + P C + (A Q - C P) = A Q + A Q = 2 A Q$
$= 10$ cm

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In fig., a circle touches the side BC of ΔABC at P and touches AS and AC produced at Q and R respectively. If AQ = 5 cm, find the perimeter of ΔABC.

The correct option is B 10 cmAQ=5 cm=AR (tangents drawn from the same external point are equal in length)Also, BP=BQ and CP=CRPerimeter of △ABC=AB+BC+AC=AB+(BP+PC)+(AR−CR)=(AB+BP)+PC+(AR−CR)=(AB+BP)+PC+(AQ−CP)=AQ+AQ=2AQ =10cm

In fig., a circle touches the side BC of $Δ A B C$ at P and touches AS and AC produced at Q and R respectively. If AQ = 5 cm, find the perimeter of $Δ A B C$ .