Tangent Lines (P3)

Drag the green dots to see the theorems at work.

THEOREM: (The Hat Theorem) If two tangent segments to a circle share a common endpoint outside the circle, then the two segments are congruent.


A) Restate this theorem in your own words. B) Why do you think it's called the hat theorem? C) Does theorem only work if the "hat" is on top of the circle? (Move the green dots to move the hat)

THEOREM: The angle formed by a tangent line and a secant line is half of the difference of the intercepted arcs.


A) Restate the theorem in your own words. B) If the angle formed by the tangent and secant is A, and the two intercepted arcs are B and C, what is the relationship between A, B, and C? (State the equation). C) Do you think that this theorem still applies if the angle is formed by two tangents? (Like in the picture from the Hat Theorem).