Track / Stage 4 / 173 of 340 #433 of 2000

Problem 433

AMC 12 late, AIME early

Geometry Difficulty 4.8 Find the answer

5. On the arc $A C$ of the circumcircle of an equilateral triangle $A B C$ , a point $M$ is chosen such that the lengths of the segments $M A$ and $M C$ are 3 and 4, respectively. The line $B M$ intersects the side $A C$ at point $N$ . Find the length of the segment $M N$ and the side of the triangle $A B C$ .

Your answer

Official solution

Answer: $A B=\sqrt{37} ; M N=\frac{12}{7}$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.