Finding The Triangle Area

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I have already solved this problem but not completely. Answers are 24 or 36/7

so the problem is next: We have a Triangle KMN, KM = 6, MN - KN = 2 cos< KMN = 3 / 5

I have already used cosine theorem and get 24 but i don't get what am i missing and why does it have second answer Please someone give me hint

Chapter is ABOUT AREA... I think it somehow is connected to < KMN

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The points $P = (x, y)$ such that $PK-PM = 3/5$ define a hyperbola so there are infinitely many of these points. However, an angle $\angle{KMN}$ given determines two points $N$ and $N'$ which in turn determine two triangles with different areas as shown in the attached figure.

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Then there are in fact two answers to the problem.