Geometry Section 10.4 Angles Formed by Secants and Tangents

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Presentation transcript:

Geometry Section 10.4 Angles Formed by Secants and Tangents

The location of an angle’s vertex determines the relationship between the angle and its intercepted arcs. I. Vertex at the II. Vertex on the circle center

The location of an angle’s vertex determines the relationship between the angle and its intercepted arcs. I. Vertex at the II. Vertex on the circle center

The location of an angle’s vertex determines the relationship between the angle and its intercepted arcs. I. Vertex at the II. Vertex on the circle center

Theorem 10.12: If a chord and a tangent intersect at a point on the circle, then the measure of the angle formed is equal to ½ the measure of the intercepted arc.

III. Vertex inside the circle

Theorem 10.13: The measure of an angle formed by two chords that intersect inside a circle is equal to ½ the sum of the two arcs intercepted by the angle and its vertical angle.

IV. Vertex outside the circle

Theorem 10.14 The measure of an angle formed by two lines that intersect outside a circle is equal to ½ the difference of the two intercepted arcs.