iran-konkur 2014 Q129

iran-konkur · Other · konkur-riazi_1393 Not Maths
129- In triangle $ABC$, $AC = 6$, $BM = 5$, and $M$ is the midpoint of $AC$. The bisectors of angles $AMB$ and $CMB$ intersect the other two sides of this triangle at $P$ and $Q$ respectively. What is the length $PQ$?
(1) $3.25$ (2) $3.5$ (3) $3.75$ (4) $4$
[Figure: Circle with inscribed quadrilateral $ADBC$, point $M$ inside, with diagonals drawn]
\textbf{129-} In triangle $ABC$, $AC = 6$, $BM = 5$, and $M$ is the midpoint of $AC$. The bisectors of angles $AMB$ and $CMB$ intersect the other two sides of this triangle at $P$ and $Q$ respectively. What is the length $PQ$?

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(1) $3.25$ \hfill (2) $3.5$ \hfill (3) $3.75$ \hfill (4) $4$

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\textit{[Figure: Circle with inscribed quadrilateral $ADBC$, point $M$ inside, with diagonals drawn]}