Question

If $ABCD$ is a cyclic quadrilateral, $AB=204,BC=104,CD=195,DA=85$ and $BD=221$, then $AC=$________

• A. $240$
• B. $225$
• C. $220$
• D. $210$

Answer 1

The correct option is C $220$

In any cycle quadrilateral, the ratio of the diagonal is equal to the ratio of the sums of products of the sides that share the diagonal and points.

i.e $AB,BC=(AB,AD+BC,CD):$

$(AB,BC+AD,CD)$

Now substituting the above values,

$AC:221=(204\times 85+104\times 195)/$ $(204\times 104\times 195)$

$(17340+20280)/(21216+16575)$

$AC:221=\frac{37620}{37791}$

$AC=\frac{37620\times 221}{37791}=220$

$AC=220$

Option $\left(c\right)$ is correct