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Lesson 6.1 Tangents to Circles Goal 1 Communicating About Circles Goal 2 Using Properties of Tangents

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Communicating About Circles Circle Terminology: A CIRCLE is the set of all points in the plane that are a given distance from a given point. The given point is called the CENTER of the circle. A circle is named by its center point. “ Circle A ” or A

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Communicating About Circles Radius Chord Diameter Tangent Secant Parts of a Circle Point of Tangency

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Communicating About Circles Tell whether each segment is best described as a chord, secant, tangent, diameter, or radius Secant A Radius Chord Diameter

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Communicating About Circles In a plane, two circles can intersect in two points, one point, or no points. Two Points One Point No Point Coplanar Circles that intersect in one point are called Tangent Circles

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Communicating About Circles Tangent Circles A line tangent to two coplanar circles is called a Common Tangent

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Communicating About Circles Concentric Circles Two or more coplanar circles that share the same center.

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Communicating About Circles Common Internal Tangents Common External Tangents Common External Tangent does not intersect the segment joining the centers of the two circles. Common Internal Tangent intersects the segment joining the centers of the two circles.

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Communicating About Circles A circle divides a plane into three parts 1.Interior 2.Exterior 3.On the circle

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Communicating About Circles Tell whether the common tangent, CB is Internal or External. External C

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Center G: (2, 2) Radius = 2 Center H: (6, 2) Radius = 2 Common tangents: x = 4; y = 4; and y = 0 Communicating About Circles Find the center and radius of each circle. Describe the intersection of the two circles and describe all common tangents.

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Using Properties of Tangents If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. Radius to a Tangent Conjecture The Converse then states: In a plane, if a line is perpendicular to a radius of a circle at the endpoint on the circle, then the line is a tangent of the circle.

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Using Properties of Tangents Is TS tangent to R? Explain If the Pythagorean Theorem works then the triangle is a right triangle TS is tangent ? ? NO!

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Using Properties of Tangents You are standing 14 feet from a water tower. The distance from you to a point of tangency on the tower is 28 feet. What is the radius of the water tower? Radius = 21 feet Tower

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Using Properties of Tangents If two segments from the same exterior point are tangent to the circle, then they are congruent. Tangent Segments Conjecture

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Using Properties of Tangents x is tangent to R at S. is tangent to R at V. Find the value of x.

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Using Properties of Tangents Find the values of x, y, and z. All radii are = y = 15 Tangent segments are = z = 36

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