Problem 1 is a construction. Problem 2 is a proof. Answer both. Follow the instructions in each case.

Carry out this construction with straightedge and compass. Leave marks showing. Label and describe the main steps of the construction as you go. (For example, F is the intersection of the perpendicular bisector of AB with the line CD.) However, you do NOT have to justify WHY the construction works.

Given point B and the circle c with center A, construct the lines through B which are tangent to circle c.

Prove this theorem. You can use in your proof any of the standard theorems (not problems) from B&B about similar triangles, right triangles, parallel lines; in other words, the theorems (Principles) from the first four chapters of B&B. You may not use (without proof) any homework problem that is not a theorem in B&B, especially not homework problems that are equivalent to this problem (of course).

Let ABC be a right triangle, with angle A the right angle. Prove that point M, the midpoint of the hypotenuse of ABC, is equidistant from the 3 vertices, A, B, C.