Q. 44.8( 4 Votes )

In the given figure, AD and AE are the tangents to a circle with center O and BC touches the circle at F. If AE = 5 cm then perimeter of ΔABC is


A. 15 cm

B. 10 cm

C. 22.5 cm

D. 20 cm

Answer :

Given : From an external point A, two tangents, AD and AE are drawn to a circle with center O. At a point F on the circle tangent is drawn which intersects AE and AD at B and C, respectively. And AE = 5 cm


To Find : Perimeter of ABC


As we know that, Tangents drawn from an external point to a circle are equal.


So we have


BE = BF …[1]


[Tangents from point B]


CF = CD …[2]


[Tangents from point C]


Now Perimeter of Triangle abc


= AB + BC + AC


= AB + BF + CF + AC


= AB + BE + CD + AC …[From 1 and 2]


= AE + AD


Now,


AE = AD = 5 cm as tangents drawn from an external point to a circle are equal


So we have


Perimeter = AE + AD = 5 + 5 = 10 cm

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