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Question

From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA $$=$$ 10 cm, find the the perimeter of the $$ \Delta PCD$$.


A
10 cm
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B
15 cm
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C
20 cm
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D
25 cm
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Solution

The correct option is C 20 cm
Let $$AC$$ and $$BD$$ be $$x$$ and $$y$$ respectively.
So, $$CE$$ and $$ED$$ will also be $$x$$ and $$y$$ respectively.....(Tangents from the same point are equal).
Since $$AC$$ and $$BD$$ are $$x$$ and $$y$$ then $$PC$$ and $$PD$$ will be $$10-x$$ and $$10-y$$ respectively.
Perimeter of triangle $$PCD$$= $$PC+PD+CD= 10-x+10-y+x+y=20  cm$$
Hence, option $$C$$ is the correct answer.

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Mathematics

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