User:Mathcounts7373

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An AOPS user with a passion for math

[asy] size(15cm);  draw((0,0)--(5,8.66025404)--(15,8.66025404)--(10,0)--cycle, purple + linewidth(3)); draw((-20,8.66025404)--(15,8.66025404)); draw((10,0)--(0,-2 * 8.66025404)); draw((-13,8.66025404)--(7.22,-4.80977186),black+linewidth(3)); draw((10,0)--(-13,8.66025404)); draw((5,8.66025404)--(7.22,-4.80977186)); draw(circle((-4,3.44),10.40288),green+linewidth(3)); draw((10,0)--(2.5,1.5 * 8.66025404)); draw((-4,3.44)--(10,0)--(5,8.66025404)--cycle,red+linewidth(3)); draw((-13,8.66025404)--(5,8.66025404)--(6.21,1.45)--cycle,blue+linewidth(3)); draw((10,0)--(6.21,1.45),orange+linewidth(3));  dot((5,8.66025404)); dot((15,8.66025404)); dot((10,0)); dot((0,0)); dot((-13,8.66025404)); dot((7.22,-4.80977186)); dot((6.21,1.45)); dot((-4,3.44));  label("$A$",(5,8.66025404),NE); label("$B$",(15,8.66025404),NE); label("$C$",(10,0),SE); label("$D$",(0,0),SW); label("$E$",(-13,8.66025404),NW); label("$F$",(7.22,-4.80977186),ESE); label("$M$",(6.21,1.45),NE); label("$O$",(-4,3.44),N); label("$k$",(-13,8.66025404)--(7.22,-4.80977186),WSW);   [/asy]

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