Secants, Tangents, & Angle Measures Section 10-6

secant – a line that intersects a circle in exactly 2 points. A secant of a circle contains a chord of the circle.

Theorem If a secant and a tangent intersect at the point of tangency, then the measure of each angle formed is one-half the measure of its intercepted arc.

60 o 120 o

Theorem If 2 secants intersect in the interior of a circle, then the measure of an angle formed is ½ the sum of the measures of the arcs intercepted by the angle and its vertical angle.

40 o 60 o 50 o

Theorem If 2 secants, a secant and a tangent, or 2 tangents intersect in the exterior of a circle, then the measure of the angle formed is ½ the positive difference of the measures of the intercepted arc.

140 o 30 o 55 o

Joke Time What is an insect that’s not feeling well? Secant (sick ant)

Who was a famous person that was not very healthy? “I sick” Newton