In the given figure, $A D a n d A E$ are the tangents to a circle with centre $O a n d B C$ touches the circle at $F$ . If $A E = 5 c m$ then perimeter of $△ A B C$ is

15 c m

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10 c m

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22.5 c m

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20 c m

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Solution

The correct option is A $15 c m$
Given $A E = 5 c m$

Perimeter of triangle $A B C = A B + B C + C A$
$= A E - B E + A D - C D + B F + C F$
As it is seen from the figure
$C D = C F, B E = B F$ (properties of tangent of circles)

$= A E + A D$ (as $A E = A D$ )
$= 5 + 5 = 10 c m$

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