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