Secants and Tangents Not Your Average Lesson. Secants Imagine being on the top of a roller coaster and the idiot next to you spits his/her gum over the.

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Presentation transcript:

Secants and Tangents Not Your Average Lesson

Secants Imagine being on the top of a roller coaster and the idiot next to you spits his/her gum over the edge... directly over the ferris wheel! The gum shoots through the ferris wheel in two locations... assuming that it doesn’t hit anyone in the process. The entire path of the gum represents a secant line. Definition: A secant is a line which intersects a circle in exactly two points

Theorem If two secants intersect inside a circle, then the angle formed by the secants is one-half the sum of the two arcs formed by the secants

“Secant” Ye Shall Find! Find the measure of angle 4

Theorem 10-5 An inscribed angle is one-half the arc it intercepts

Theorem When a secant and a tangent intersect at the point of tangency, the angle formed is one- half the measure of the intersected arc

“Secant” Ye Shall Find...AGAIN! Find the measure of angle TXY

Theorem If a combination of two secants/tangents intersect outside of a circle, the formed angle is the average of the two arcs which are formed

Find the values of X