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Angle Sum Property

If the circum...

Question

If the circumcircle of an isosceles triangle $A B C$ is equal to $A B = A C,$ then the angle $A$ is

\frac{π}{6}

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\frac{π}{3}

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\frac{π}{2}

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\frac{2 π}{3}

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Solution

The correct option is D $\frac{2 π}{3}$
$\begin{matrix} I n Δ P Q R P C = C R = C Q = R P C = P R P C = P R = C R Δ P C R i s a n e q u i l a t e r a l Δ ∠ C P R = 60^{\circ} Δ P C Q i s a n e q u i l a t e r a l Δ ∠ C P Q = 60^{\circ} ∠ P = ∠ C P Q + ∠ C P R = 120^{\circ} \end{matrix}$

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