12 Pull It All Together BIG idea Reasoning and Proof You can use triangle congruence theorems to prove relationships among tangents and secants. Task 1 Four tangents are drawn from E to two concentric circles. A, B, A C, and D are the points of tangency. Name as many pairs of congruent triangles as possible and tell how you can show each pair is congruent. E BIG idea Coordinate Geometry You can use coordinates of the center of a circle and its radius to write an equation for a circle. Task 2 A gardener wants the three rosebushes in her garden to be watered by a rotating water sprinkler. The gardener draws a diagram of the garden using a grid in which each unit represents 1 ft. The rosebushes are at (1, 3), (5, 11), and (11, 4). She wants to position the sprinkler at a point equidistant from each rosebush. Where should the gardener place the sprinkler? What equation describes the boundary of the circular region that the sprinkler will cover? 810 Chapter 12 Pull It All Together