Quandaries and Queries


My problem is as follows:
An isosceles trapezoid with bases of lengths 12 and 16 is inscribed in a circle with a radius of 10.  The center of the circle lies in the interior of the trapezoid.  Find the area of the trapezoid.

Thanks for your help!

I am a student-teacher
Grade level 9th to 12th



Hi Bruce,

The area of a traposoid is the average of the lengths of the parallel sides times the distance between the parallel lines. I drew a rough sketch of your situation.

C is the center of the circle and triangle ABC is a right triangle so you can use Pythagoras' theorem to find |AC|. Can you complete the problem now?



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