If four sides of a quadrilateral ABCD are tangential to a circle, then

Question:

If four sides of a quadrilateral ABCD are tangential to a circle, then

(a) AC + AD = BD + CD

(b) AB + CD = BC + AD

(c) AB + CD = AC + BC

(d) AC + AD = BC + DB

Solution:

The figure of the Quadrilateral is drawn below.

We know that length of the tangents drawn from an external point will be equal. Therefore,

AP = PQ

DP = DS

CR = CS

BR = BQ

Let us add all the above four equations. We get

AP + DP + CR + BR = PQ + DS + CS + BQ

By looking at the figure, we can rewrite the above equation as,

AD + BC = AB + CD

Therefore, the correct answer is option (c).

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