Question

ABCD is a cyclic quadrilateral in which AB = 16.5 cm, BC = x cm, CD = I1 cm, AD = 19.8 cm, and BD is bisected by
AC at O. What is the value of x?
Ans 13.2cm​

Answer 1

Given :

ABCD is a cyclic quadrilateral.

length of AB :

=16.5 cm

Length of CD :

= 11 cm

Length of AD :

= 19.8 cm

To Find :

Length of BC = ?

Solution :

∴For this cyclic quadrilateral ratio of area of ΔABC to area of ΔACD will be equal to the ratio of length of OB to the length of OD.

so,  $\frac{area \triangle ABC}{area \triangle ACD} =\frac{OB}{OD}$

Now , since OB = OD

Therefore , putting values in above equation it becomes :

$\frac{\frac{1}{2}\times 16.5\times x }{\frac{1}{2}\times 19.8 \times 11 } =1\\\\x = \frac{19.8 \times 11}{16.5} \\\\x= 13.2 cm$

So the value of BC i.e x is 13.2 cm