IMAS 2022–2023 — Upper Primary — Round 2 Question 15

In triangle $ABC$, $M$ is the midpoint of $BC$ and $N$ is the midpoint of $AM$. The extension of $BN$ intersects $AC$ at $K$, as shown in the figure below. If $KA=24$ cm, then what is the length, in cm, of $AC$? Give a detailed solution.