iran-konkur 2015 Q130

iran-konkur · Other · konkur-riazi_1394 Not Maths
130. In triangle $ABC$, $M$ is the midpoint of side $BC$ and $AD$ is the angle bisector of angle $A$. The circumscribed circle of triangle $ADM$ is drawn.
[Figure: Triangle ABC with point M on BC, point D on BC, points B' and C' on the circle, and the circumscribed circle of triangle ADM]
The ratio $\dfrac{BB'}{CC'}$ equals which of the following?
(1) $1$
(2) $\dfrac{AB}{AC}$
(3) $\dfrac{AB'}{AC'}$
(4) $\dfrac{DB}{DM}$
\textbf{130.} In triangle $ABC$, $M$ is the midpoint of side $BC$ and $AD$ is the angle bisector of angle $A$. The circumscribed circle of triangle $ADM$ is drawn.

\textit{[Figure: Triangle ABC with point M on BC, point D on BC, points B' and C' on the circle, and the circumscribed circle of triangle ADM]}

The ratio $\dfrac{BB'}{CC'}$ equals which of the following?

\begin{tabular}{ll}
& (1) $1$ \\
& (2) $\dfrac{AB}{AC}$ \\
& (3) $\dfrac{AB'}{AC'}$ \\
& (4) $\dfrac{DB}{DM}$
\end{tabular}