MathDB

10

Part of 1982 AMC 12/AHSME

Problems(1)

Perimeter of a triangle

Source:

1/16/2006
In the adjoining diagram, BOBO bisects ∠CBA\angle CBA, COCO bisects ∠ACB\angle ACB, and MNMN is parallel to BCBC. If AB=12AB=12, BC=24BC=24, and AC=18AC=18, then the perimeter of △AMN\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("AA", A, dir(90)); label("BB", B, dir(O--B)); label("CC", C, dir(O--C)); label("MM", M, dir(90)*dir(B--A)); label("NN", N, dir(90)*dir(A--C)); label("OO", O, dir(90));[/asy]
(A) 30(B) 33(C) 36(D) 39(E) 42\textbf {(A) } 30 \qquad \textbf {(B) } 33 \qquad \textbf {(C) } 36 \qquad \textbf {(D) } 39 \qquad \textbf {(E) } 42
geometryperimeterincenterinradiusratio