Transcript Section 1.1 - West Ada School District / Homepage

9-6
Secants, Tangents, and Angle
Measures
Objectives:
• To find the measures of angles formed by intersecting
secants and tangents in relation to intercepted arcs..
Vocabulary
• Secant
Secant
• A line that intersects a circle in exactly two
points is called a secant of the circle.
• A secant of circle contains a chord of the
circle.
Theorem 9-11
• If a secant and a tangent
intersect at the point of
tangency, then the measure
of each angle formed is onehalf the measure of its
intercepted arc.
Theorem 9-12
• If two secants intersect in the
interior of a circle, then the
measure of an angle formed is
one-half the sum of the
measures of the arcs
intercepted by the angle and its
vertical angle.
Example 1
• Find the value of x.
• Find the measure of
angle AET.
Theorem 9-13
Case 1 – Two Secants
• If two secants, a secant and a
tangent, or two tangents
intersect in the exterior of a
circle, then the measure of the
angle formed is one-half the
positive difference of the
measures of the intercepted
arcs.
Example 2
Theorem 9-13
Case 2 – A Secant and a Tangent
• If two secants, a secant and a
tangent, or two tangents
intersect in the exterior of a
circle, then the measure of the
angle formed is one-half the
positive difference of the
measures of the intercepted
arcs.
Example 3
Theorem 9-13
Case 3 – Two Tangents
• If two secants, a secant and a
tangent, or two tangents
intersect in the exterior of a
circle, then the measure of the
angle formed is one-half the
positive difference of the
measures of the intercepted
arcs.
Example 4