Tangents to CirclesCircles

Secants and Tangents Secant 2 points of intersection Tangent 1 point of intersection Point of Tangency

Radii _|_ Chord What would you conclude about the following diagram? P A B X R

Radii _|_ Chord What would you conclude about the following diagram? P A B X R AX  XB ? Prove it!

Radii & Tangent What would you conclude about the following diagram? P A

Radii & Tangent Does this help?? P A

Radii & Tangent The tangent is perpendicular to the radius at the point of tangency P A

Inscribed Angles & Arcs An inscribed angle has its vertex ON the circle.

Inscribed Angles & Arcs An inscribed angle has its vertex ON the circle. Intercepted arc

Inscribed Angles & Arcs What type of inscribed angle forms a minor arc? Minor arc

Inscribed Angles & Arcs What type of inscribed angle forms a major arc? Major arc

Inscribed Angles & Arcs What type of inscribed angle forms a semicircle? Semicircle

Inscribed Angle Theorem An angle inscribed in an arc has a measure equal to ½ the measure of the intercepted arc. 60 120

Inscribed Angle Theorem What is the missing measure? 20 ??

Inscribed Angle Theorem What is the missing measure? 90 ??

Inscribed Angle Theorem What is the missing measure? ??

Inscribed Angle Theorem What is the missing measure? 40 ??

Theorem If two inscribed angles intercept the same arc, then they have the same measure 40 80