Question

ABCD is a cyclic quadrilateral. If the length of AB, BC, CD and AD are 8, 6, 7, and 5 cm respectively, then AC$\times$BD = .

• A. 86 ${cm}^2$
• B. 56 ${cm}^2$
• C. 48 ${cm}^2$
• D. 96 ${cm}^2$

Answer 1

The correct option is A 86 ${cm}^2$


Given: ABCD is a cyclic quadrilateral.
AB = 8 cm,
BC = 6 cm,
CD = 7 cm,
AD = 5 cm.

We know that, in a cyclic quadrilateral the product of the length of its diagonals is equal to the sum of products of the lengths of the pairs of opposite sides.
$AC\times BD=(AB\times CD)+(BC\times AD)$
$AC\times BD=(8\times 7)+(6\times 5)$
$AC\times BD=56+30=86{cm}^2.$