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Number of Tangents Drawn from a Given Point

In the given ...

Question

In the given figure, a circle touches the side $B C$ of $Δ A B C$ at $P$ and touches $A B$ and $A C$ produced at $Q$ and $R$ respectively. If $A Q = 5 c m$ , find the perimeter of $Δ A B C$

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Solution

Length of tangent drawn from external point to a circle is some
$∴ A Q = A R; B P = B Q; C P = C R; B P = P C$
$A Q = 5 c m$ ; LEt $B P$ be $x$
Perimeter of $△ A B C$
$A B + B C + C A$
$(A Q - B Q) + B C + (A R - C R)$
$(5 - x) + B P + P C + (5 - x)$
$(5 - x) + x + x + (5 - x)$
$= 10 c m$ .

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