Question

Area of
P
it the
its of
In the given figure, OPOR is a rhombus, three of
whose vertices lie on a circle with centre 0. If the
area of the rhombus is 3213 cm, find the radius
of the circle.
2017
entre
R​

Answer 1

Let radius of circle be 'r'. Then OP=OQ=OR=

′

r

′

㎝

OQ and RP are diagonals and these bisects each other at 90°

Also, RS=SP

In right △OSP,OP

2

=OS

2

+PS

2

⇒r

2

=(

2

r

)

2

+PS

2

⇒PS

2

=r

2

−

4

r

2

=

4

3r

2

⇒PS=

2

3

r⇒PR=2PS=2×

2

3

r=

3

r

Area of rhombus=32

3

㎠

⇒

2

1

×OQ×RP=32

3

⇒

2

1

×r×

3

r=32

3

⇒r

2

=64

⇒r=

64

=8㎝

Therefore, radius of circle=8㎝