Question

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

• A. AC + AD = BD + CD
• B. AB + CD = BC + AD
• C. AB + CD = AC + BC
• D. AC + AD = BC + DB

Answer 1

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)

$\Rightarrow$ AD + BC = AB + CD.