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8-1B Circles and Tangent Lines When you have a line and a circle in the same plane, what three situations are possible? What is a secant line? What is a tangent line? What is a point of tangency? What angle is formed when a tangent line intersects a radius? If a circle has two tangent segments from the same exterior point, what is true about the segments?

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One line, One circle, Same plane…. The line does not intersect the circle in any points. Scene 1

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One line, One circle, Same plane…. Scene 2 The line intersects the circle in two points. It is a secant line.

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One line, One circle, Same plane…. Scene 3 The line intersects the circle at one point. The line is called a tangent line. The point where it touches the circle is called the Point of tangency.

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Off on a tangent Draw a circle Add two tangent lines Extend the lines until they intersect. Measure the lengths of the two tangent segments from the circle to the intersection. What do you find about the distance from the point of tangency to the point of intersection?

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Find AC. A B C 33 cm 24 cm 33 2 + 24 2 = c 2 c ≈ 40.80

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Spheres A sphere is the locus of points in space a given distance from a point call the center of the sphere. The radius of the sphere is a segment from the center to a point on the sphere. The distance from the enter to any point on the sphere is also called the radius. center radius

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Great Circle Tangent lines to spheres touch the sphere at exactly one point. A tangent line or tangent plane contains exactly one point of the sphere. A great circle is a circle on the sphere whose center is also the center of the sphere. center Great circle

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Theorems about tangents to a circle If a line is tangent to a circle, then it is perpendicular to a radius at the point of tangency. If a line coplanar to a circle is perpendicular to a radius of a circle at point on the circle, then the line is tangent to the circle. Two tangent segments to a circle from the same exterior point are congruent.

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When you have a line and a circle in the same plane, what three situations are possible? 0,1,or 2 points of intersection What is a secant line? A line intersects the circle in two points. What is a tangent line? A line intersects the circle at one point. What is a point of tangency? The point where the tangent line touches the circle.

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What angle is formed when a tangent line intersects a radius? 90° If a circle has two tangent segments from the same exterior point, what is true about the segments? The segments are congruent.

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Assignment 8-1B Page 547, 1-11, 13-16, 20-23

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