isi-entrance 2014 Q22

isi-entrance · India · solved Sine and Cosine Rules Circumradius or incircle radius computation

In a triangle $ABC$, the circumradius is $r$ and $BC = r/2$. The circumcentre $O$ lies on $AD$ where $D$ is the midpoint of $BC$. Find the ratio $BC : AD$.
(A) $\sqrt{3} : \sqrt{2}$ (B) $\sqrt{2} : \sqrt{3}$ (C) $1 : \sqrt{3}$ (D) $\sqrt{3} : 1$

(A) $BC : AD = \sqrt{3} : \sqrt{2}$

In a triangle $ABC$, the circumradius is $r$ and $BC = r/2$. The circumcentre $O$ lies on $AD$ where $D$ is the midpoint of $BC$. Find the ratio $BC : AD$.

(A) $\sqrt{3} : \sqrt{2}$ \quad (B) $\sqrt{2} : \sqrt{3}$ \quad (C) $1 : \sqrt{3}$ \quad (D) $\sqrt{3} : 1$

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