Question

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, 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.

Two concentric circles have center O, with point E outside. From O, segments lead to B and C on the inner circle and A and B on the outer circle, with segments AB and CD connecting the circles. Segments from E lead to A, B, O, C, and C.

BIG idea: Measurement
You can use facts about arcs and angle measures to solve real-world problems.

Task 2
The rocks near the shore between two lighthouses at points A and B make the waters unsafe. The measure of AXB⏜ modified eh x b with frown above is 300. Waters inside this arc are unsafe. Suppose you are a navigator on a ship at sea. How can you use the lighthouses to keep the ship in safe waters?

A portion of a circle connects points A and B on a shore, with point X on the portion closer to A.