TJ Prep Problems

TJ test prep practice problems  for our students and readers. The problems provide a very small sampling of what Optimal TJ Prep students work with.

A Difficult Geometry Problem for TJ/AOS/Blair Prep. Target Time. 25-120 seconds.

In the figure below, a right triangle ABC is shown.a circle is drawn with diameter AC and half of the circle is shaded blue.  Two semicircles are drawn with diameters a and c. The region between the circle and the semicircles are shaded green. What is the area of the green regions? What is the ratio of the green regions to the blue region?