Question

3. In the given figure, OABC is rhombus. Find angle AOB
and angle BOC, where 'O' is the centre of circle.

Answer 1

Answer:

Let the r be the radius of the circle.

∴OA=OB=OC=r ...(I)

□OABC is a rombus.

∴OA=AB=BC=OC ...(II)

From (i) and (ii) we get,

OA=OB=AB=BC=OC=r

Thus,

△OAB and △OBC are equilateral triangle having each side r meter.

Also, we know that diagonal of a parallelogram divides it into two triangles of equal areas.

∴ Area of △OBC= Area of △OAB ...(iii)

Area of a rhombus OABC=32

3

m

2

Area of △OAB+ Area of △OBC=32

3

m

2

2× Area of △OAB=32

3

m

2

2×

4

3

r

2

=32

3

m

2

=>r

2

=64

=>r=8m