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Secants, Tangents, & Angle Measures Section 10-6

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

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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.

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60 o 120 o

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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.

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40 o 60 o 50 o

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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.

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140 o 30 o 55 o

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

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

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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?

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?

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