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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