Calculate the unknown Area in the semi circle | Geometry Math Problem | GeoGebra

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[holyshit]

It would be easier if we draw radius to this vertex outside diameter
then we can use formulas for area of this two triangles
and Pythagorean identity in triangle created by drawing radius
But solution presented on video is even better

[GoogleAccount-pict]

My solution:
Notice that they have the same height but one has 4 times the area of other. Thus a = 4b.

By power of a point (mirror semicircle around line), sqrt(ab) is the height.

sqrt(ab) = sqrt(4b^2) = 2b.

By area of a triangle, b^2 = 9. Therefore b = 3, a = 12, r = 15/2, area will be 225pi/8 - 45