A quadrilateral is inscribed in a circle. If the opposite angles of the quadrilateral are equal and length of its adjacent sides are 6 cm. and 8 cm., what is the area of the circle?

The sum of opposite angles of a cycle quadrilateral is 180°.

$herefore angle mathrm{A}=angle mathrm{B}=angle mathrm{C}=angle mathrm{D}=90^{circ}$

$herefore mathrm{ABCD}$ is a rectangle.

$mathrm{AB}=8 mathrm{~cm} ., mathrm{BC}=6 mathrm{~cm} .$

$herefore mathrm{AC}=sqrt{mathrm{AB}^{2}+mathrm{BC}^{2}}$

$=sqrt{8^{2}+6^{2}}=sqrt{64+36}=sqrt{100}=10 mathrm{~cm} .$

$herefore$ Radius of circle $=5 mathrm{~cm} .$

$herefore$ Area of circle $=pi r^{2}$

$=pi imes 5 imes 5=25 pi$ sq. $mathrm{cm} .$