Geometry Foundation Quiz #1 Q10

Hello, could someone explain how to solve this problem? I was able to create a 30 60 90 triangle by drawing a perpendicular line from point A to line segment AB. This allowed me to figure out the height of the triangle. When solving for the remainder of the base (segment AB), I got stuck; we do not know the rest of the interior angles of the second / right half of the divided triangle aside from a 90 degree angle.

Is there some rule about inscribed angles / triangles that I am missing? How can you solve this problem?

Thank you in advance for your help!

Yes you do - \Delta ACB itself is 30-60-90!

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The angle inscribed by the diameter of a circle on the circumference is a right angle. So angle ACB is now 90 degrees, and voila, BC and AC are now height and base interchangeably. Now apply the 30-60-90 rule to find the sides and then the area.

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