If the four sides of a quadrilateral $A B C D$ are tangential to a circle, which of the following is true?

A C + A D = B D + C D

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A B + C D = B C + A D

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A B + C D = A C + B D

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A C + A D = B C + A B

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Solution

The correct option is B $A B + C D = B C + A D$

Let ABCD be the points where the circle touches the quadrilateral
From a point out side of the circle the two tangents to the circle are equal.
AP = AS, BP = BQ , CR = CQ , and DR = DS
Adding AP + BP + CR + DR = AS + BQ + CQ + DS
AB + CD = AD + BC

So, option B is the answer.

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