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Question

If a quadrilateral ABCD is drawn to circumscribe a circle, then which of the options is true?


A

AC + AD = BD + CD

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B

AB + CD = BC + AD

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C

AB + CD = AC + BC

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D

AC + AD = BC + DB

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Solution

The correct option is B

AB + CD = BC + AD



We know that , tangents drawn from a point outside the circle are equal in length.

So,
AS = AP

BQ = BP

CQ = CR

DS = DR

On adding the above equations we get,

AS + BQ + CQ + DS = AP + BP + CR + DR

(AS + DS) + (BQ + CQ) = (AP + BP) + (CR + DR)

AD + BC = AB + CD.


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