Secant-Tangent AnglesSecant-Tangent Angles

Chapter 14Chapter 14

Section 4Section 4

What is a Secant-Tangent Angle?What is a Secant-Tangent Angle?

Secant-Tangent angles are formed Secant-Tangent angles are formed when a secant line intersects a when a secant line intersects a tangent line in one of two ways:tangent line in one of two ways:

1. On the circle1. On the circle

2. Exterior of the circle2. Exterior of the circle

Vertex Outside the CircleVertex Outside the Circle

Theorem 14-10 says that if the vertex of Theorem 14-10 says that if the vertex of a secant-tangent angle is outside the a secant-tangent angle is outside the circle, then its degree measure is half circle, then its degree measure is half the difference of the intercepted arcs.the difference of the intercepted arcs.

Think: Big arc – Little arc then divide by two.Think: Big arc – Little arc then divide by two.

Big ArcLittle Arc

Vertex On The CircleVertex On The Circle

Theorem 14-11 says that if a secant-Theorem 14-11 says that if a secant-tangent angle has a vertex on the tangent angle has a vertex on the circle, then its vertex is half the degree circle, then its vertex is half the degree measure of the intercepted arc.measure of the intercepted arc.

Intercepted Arc

Think:

Intercepted Arc Intercepted Arc divided by two.divided by two.

What if both lines are tangent?What if both lines are tangent?

Theorem 14-12 says that when a Theorem 14-12 says that when a tangent-tangent angle is formed, the tangent-tangent angle is formed, the degree measure is half the difference degree measure is half the difference of the intercepted arcs.of the intercepted arcs.

Big Arc

Little Arc

Think: Big arc – Little arc Think: Big arc – Little arc then divide by two.then divide by two.