Question

If the radius of the circumcircle of an isosceles triangle ABC is equal to R and AB$=$AC$=$R, then the angle A is equal to?

• A. $\pi /6$
• B. $\pi /3$
• C. $\pi /2$
• D. $2\pi /3$

Answer 1

Answer: (D)

$2\pi /3$

$R$ is circum circle, $AB=AC=R$

$\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}=\frac{1}{2R}$

$sinB=sinC=\frac{R}{2R}=\frac{1}{2}=\sin 30$

$B=C={30}^0$

So, $A=180-30-30={120}^0=\frac{2\pi }{3}$ (Answer D)