# Reach for the Summit - M-S5-A1

Geometry Level 3

In $\triangle ABC$, $A(3,4)$, $B(-5,0)$, $M(0,0)$, $N(2,0)$, $C$ is a point on the positive $x$-axis such that $\angle BAM = \angle CAN$.

If the circumcenters of $\triangle AMN$ and $\triangle ABC$ are $D(x_1,y_1)$ and $E(x_2,y_2)$ respectively, find $\lfloor 1000(x_1+2y_1+3x_2+4y_2)\rfloor$.

Hint: Find the relationship of $AD$ and $AE$.

Reach for the Summit problem set - Mathematics

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