Question

In the given figure, a circle touches all the four sides of a quadrilateral ABCD with AB = 12cm, BC = 10 cm and CD = 14cm. Find AD.

• A. 10
• B. 12
• C. 15
• D. 16

Answer 1

The correct option is D 16



Let AD =x, then BD = (12-x)
AD' = AG = x [ Tangents drawn from the same external point are equal to each other.]
Similarly,
BD = BE = (12-x),
Then CE = 10- (12-x) =x-2
CE = CF =(x-2) [ Tangents drawn from the same external point are equal to each other.]
FD = 14 - (x-2) = (16 - x)
Similarly,
FD = DG = (16 - x)
AD = AG + GD = x + 16-x =16 cm