what information is missing?

Note: In order to receive full points, you must show all your work. 1. Using the sides a, b, c of a given triangle ABC as bases, construct three equilateral triangles outward. (Note: The result holds true even if we were to construct the equilateral triangles inward, but for the sake of simplicity we will cover only the outward construction.) Let D, E, F be the third vertices of the equilateral triangles DAB, EBC, FCA, respectively. Let K, L, M be the circumcenters of these same equilateral triangles, respectively. We will show that triangle KLM is equilateral. For simplicity we will assume that triangle ABC is acute. (This theorem is usually attributed to Napoleon.) a) Use coordinates to set the triangle ABC on the plane. b) For a random equilateral triangle of side a, show that its circumcenter is on the perpendicular bisector of its base at a distance of a 3/6 from the base. c) Using the results of (a) and (b) above to find the coordinates of K, L, M. (Hint: Let the coordinates of point k be (x, y). Using (b) and the fact that KB = KA you get two equations with two unknows.) d) Prove that triangle KLM is equilateral. a2+2+c2 e) Show that the side of this equilateral triangle KLM is given by + a, b, c, E are the sides and area of the triangle, respectively. Note: In order to receive full points, you must show all your work. 1. Using the sides a, b, c of a given triangle ABC as bases, construct three equilateral triangles outward. (Note: The result holds true even if we were to construct the equilateral triangles inward, but for the sake of simplicity we will cover only the outward construction.) Let D, E, F be the third vertices of the equilateral triangles DAB, EBC, FCA, respectively. Let K, L, M be the circumcenters of these same equilateral triangles, respectively. We will show that triangle KLM is equilateral. For simplicity we will assume that triangle ABC is acute. (This theorem is usually attributed to Napoleon.) a) Use coordinates to set the triangle ABC on the plane. b) For a random equilateral triangle of side a, show that its circumcenter is on the perpendicular bisector of its base at a distance of a 3/6 from the base. c) Using the results of (a) and (b) above to find the coordinates of K, L, M. (Hint: Let the coordinates of point k be (x, y). Using (b) and the fact that KB = KA you get two equations with two unknows.) d) Prove that triangle KLM is equilateral. a2+2+c2 e) Show that the side of this equilateral triangle KLM is given by + a, b, c, E are the sides and area of the triangle, respectively