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.

(4)

A) Restate this theorem in your own words. [br][br]B) Why do you think it's called the hat theorem?[br][br]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.

(5)

A) Restate the theorem in your own words. [br][br]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).[br][br]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).

Tangent Lines (P3)

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

(4)

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

(5)

Information: Tangent Lines (P3)