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This guide explores the angles formed by secants and tangents relative to circles. It explains three positions of vertices: on the circle, inside, and outside the circle, detailing the measures of angles in each case. By applying key theorems, you can find the angles formed by tangent-secant intersections, chords intersecting inside the circle, and secants meeting outside the circle. Practical examples illustrate these concepts, enabling a comprehensive understanding of circle geometry and angle relationships within circular functions.
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10.4: Angles formed by Secants and Tangents Obj: ______________________ __________________________
Vertex is ON the circle • 1) 2)
Vertex is OUTSIDE the circle • 1) 2) 3)
Theorem • If a tangent and a secant (or a chord) intersect on a circle at the point of tangency, then the measure of the angle formed is __________ the measure of its intercepted arc.
Theorem • The measure of an angle formed by two secants or chords intersecting in the interior of a circle is _______________ the ______________ of the measures of the intercepted arcs.
The measure of an angle formed by two secants in the exterior of a circle is __________ the measures of the intercepted arcs.
The measure of a secant-tangent angle with its vertex outside the circle is ____________ _____________________________________
The measure of a tangent-tangent angle with • its vertex outside the circle is ____________ • _____________________________________
