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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 10.13 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 10.12 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 10.14 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
Secants, Tangents, and Angle Measures
Classifying Angles with Circles
Section 10.5 Angles in Circles.
Geometry Warm-Up4/5/11 1)Find x.2) Determine whether QR is a tangent.
Other Angle Relationships
Other Angle Relationships in Circles Section 10.4
Apply Other Angle Relationships in Circles
SECANTS Secant - A line that intersects the circle at two points.
10.4: Angles formed by Secants and Tangents Obj: ______________________ __________________________.
6.5 Other Angle Relationships in Circles. Theorem 6.13 If a tangent and a chord intersect at a point on the circle, then the measure of each angle formed.
Geometry Section 10.4 Angles Formed by Secants and Tangents
Arcs and Angles Continued
6.5Apply Other Angle Relationships Theorem 6.13 If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one.
Section 10.4 Other Angle Relationships in Circles.
Secants, Tangents and Angle Measures. Definition - Secant.
Angles Formed by Tangents, Chords, and Secants
Secants, Tangents and Angle Measures
You have learned how to find the measures of central angles and inscribed angles in circles. What if an angle is not inscribed and its not a central angle?
10.4 Other Angles Relationships In Circles. Theorem A tangent and a chord intersect at a point, it makes angles that are ½ the intercepted arc.
6.5 Apply other Angle Relationships in Circles
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