Question

AB is a chord of a circle with centre O. If $\angle AOB={70}^{\circ }$ and AB=16 cm, the diameter of the circle will be $[sin{35}^{\circ }=0.57]$

• A. 32.2 cm
• B. 30.8 cm
• C. 26.4 cm
• D. 28.07 cm

Answer 1

The correct option is D

28.07 cm

Draw diameter AC passing through center O.

$\angle BOC=180-\left({70}^{\circ }\right)={110}^{\circ }$

$\because \angle OBC=\angle OCB$ (as OB=OC,isosceles triangle)

$\angle OBC=\angle OCB=\frac{(180-{110}^{\circ })}{2}={35}^{\circ }$

In right-angled triangle ABC

$sin{35}^{\circ }=\frac{AB}{AC}$

$AC=\frac{AB}{sin{35}^{\circ }}=\frac{16}{0.57}=28.07cm$

So, diameter AC=28.07 cm