[ Law of Cosines

A right triangle $ABC$ is inscribed in a circle. A chord $CM$ is drawn from vertex $C$ of the right angle, intersecting the hypotenuse at point $K$. Find the area of triangle $ABM$, if $BK: AB=3: 4, BC=2 \sqrt{2}, AC=$

4. 

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Apply the theorem of the products of segments of intersecting chords.

## Answer

$\frac{36}{19} \sqrt{2}$.