Use inversion to solve the following problem: Let AC and BC be lines that meet at a right angle at C. Let X be a point between A and C and let Y be a point between B and C. Let a and a be the circles centered at A and X and passing through C. Let B1 and B2 be the circles centered at B and Y and passing through C. Let D, E, F, G be the points of intersection of the alpha circles with the beta circles. Use the following steps to prove that D, E, F, G lie on a common circle. 1. Create a circle of inversion omega that will make the problem easier. Explain what you predict the inverted circles will look like and why. 2. Use the Reflect about Circle tool to invert the diagram and check your prediction. Then prove that D', E, F, G' lie on a common circle. (If this is not easier than the original problem, try a different circle of inversion.) 3. Explain why D, E, F, G must also lie on a common circle.