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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 ΔPCD.

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 10x and 10y respectively.
Perimeter of triangle PCD= PC+PD+CD=10x+10y+x+y=20cm
Hence, option C is the correct answer.

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