SSC
SSC CHSL TIER-I Solved Paper Held on 07.01.2017
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 \[=\pi {{r}^{2}}\] \[=\pi \times 5\times 5=225\,sq.\,cm.\]