question_answer

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?

A) \[64\pi \,sq\,.cm.\]

B) \[25\pi \,sq\,.cm.\]

C) \[36\pi \,sq\,.cm.\]

D) \[49\pi \,sq\,.cm.\]   

Correct Answer: B

Solution :

The sum of opposite angles of a cycle quadrilateral is\[{{180}^{o}}\]. \[\therefore \]\[\angle A=\angle B=\angle C=\angle D=90{}^\circ \] \[\therefore \] ABCD is a rectangle. AB = 8 cm., BC = 6 cm. \[\therefore \]\[AC=\sqrt{A{{B}^{2}}+B{{C}^{2}}}\] \[=\sqrt{{{8}^{2}}+{{6}^{2}}}=\sqrt{64+36}=\sqrt{100}\] = 10 cm. \[\therefore \]Radius of circle = 5 cm. \[\therefore \]Area of circle \[=\pi {{r}^{2}}\] \[=\pi \times 5\times 5=225\,sq.\,cm.\]