Question

$ABCD$ is a quadrilateral, the sides of which touch a circle. Which one of the following is correct?

• A. $AB+AD=CB+CD$
• B. $AB:CD=AD:BC$
• C. $AB+CD=AD+BC$
• D. $AB:AD=CB:CD$

Answer 1

The correct option is C $AB+CD=AD+BC$

Let $ABCD$ be the quadrilateral.

In this situation, sum of the opposite sides is equal.
$AL=AT$ ..... (i)
$LB=BM$ .... (ii)
$DT=DN$ .... (iii)
$NC=MC$ .... (iv)
Therefore, $(DN+NC)+(AL+LB)$
$=DT+MC+AT+BM$
Thus $DC+AB=BC+AD$