Problem

1982 AHSME Problem 10

In the adjoining diagram, $BO$ bisects $\angle CBA$ , $CO$ bisects $\angle ACB$ , and $MN$ is parallel to $BC$ . If $AB=12, BC=24$ , and $AC=18$ , then the perimeter of $\triangle AMN$ is

[asy] size(200); defaultpen(linewidth(0.7)+fontsize(10)); pair B=origin, C=(24,0), A=intersectionpoints(Circle(B,12), Circle(C,18))[0], O=incenter(A,B,C), M=intersectionpoint(A--B, O--O+40*dir(180)), N=intersectionpoint(A--C, O--O+40*dir(0)); draw(B--M--O--B--C--O--N--C^^N--A--M); label("$A$", A, dir(90)); label("$B$", B, dir(O--B)); label("$C$", C, dir(O--C)); label("$M$", M, dir(90)*dir(B--A)); label("$N$", N, dir(90)*dir(A--C)); label("$O$", O, dir(90));[/asy]

$\text {(A)} 30 \qquad \text {(B)} 33 \qquad \text {(C)} 36 \qquad \text {(D)} 39 \qquad \text {(E)} 42$

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

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Category: AHSME
Points: 1
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