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1985 AMC 12 Question 3

AMC12 · 1985 AMC 12

Question 3

In right $\triangle ABC$ with legs $5$ and $12,$ arcs of circles are drawn, one with center $A$ and radius $12,$ the other with center $B$ and radius $5.$ They intersect the hypotenuse in $M$ and $N.$ Then $MN$ has length

Question illustration
  1. $2$
  2. $\frac{13}{5}$
  3. $3$
  4. $4$
  5. $\frac{24}{5}$