Question

If one side of a triangle is 12 cm and the opposite angle is 30 degrees, then the diameter of the circumscribed circle is :

• A. 18 cm
• B. 30 cm
• C. 24 cm
• D. 20 cm
• E. none of these.

Answer 1

Answer: (C)

24 cm

R.E.F image

Given : $\angle ACB={30}^{\circ }$

$AB=12cm$

Find :- diameter of

circle.

Solution :

We know that in a circle the measure

of central angle is twice the measure of

the inscribed angle that intercepts the same.

so $\angle AOB=2\angle ACB$

$=2\times {30}^{\circ }={60}^{\circ }$

Draw a line $OD$ which is divide the angle

and $AB$ line in equal two parts.

so $\angle BOD={30}^{\circ }$ & $\angle ODB={90}^{\circ }$

$\angle OBD={60}^{\circ }$ & $BD=6cm$

By trigonometry rule.

$\cos B=\frac{BD}{OB}$

$\cos {60}^{\circ }=\frac{6CM}{OB}$

$OB=6\times 2=12cm$

$OB$ is radius of circle so diameter of

circle is $2\times OB$

$=2\times 12=24cm$