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
B
15 cm
C
20 cm
D
25 cm

Solution

## The correct option is C 20 cmLet $$AC$$ 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.Mathematics

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