The PDF linked below challenges a student to use geometric properties of circles and triangles to prove that two triangles are congruent. A student must be able to use congruency and corresponding parts to reason about lengths of sides. A student must be able to construct lines to make sense of a diagram. A student needs to use geometric properties to find the radius of a circle inscribed in a right triangle.
http://www.insidemathematics.org/common-core-math-tasks/high-school/HS-G-2007%20Circles%20in%20Triangles.pdf