Can You Find the Shaded Area Without Finding the Radius?

In this geometry problem, we find the area of a shaded circle inside a larger semicircle using a clever combination of circle theorems and the Pythagorean theorem. We’ll work step by step, first finding the large semicircle’s diameter and radius, then using the perpendicular from the small circle’s center to a chord to create useful right triangles. The key is connecting these triangles and eliminating the unknown distances until we reach r² = 11. From there, the shaded area follows immediately: 11π square units, or approximately 34.56 square units. This is a great problem for students studying high school geometry, SAT/ACT math, competitive mathematics, and circle theorems. Follow along and see if you can spot the key relationship before the final step! #Geometry #MathProblem #CircleGeometry #PythagoreanTheorem #MathTutorial