Presentation on theme: "Lesson 6.1 Tangents to Circles"— Presentation transcript:
1Lesson 6.1 Tangents to Circles Goal Communicating About CirclesGoal Using Properties of Tangents
2Communicating 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
3Parts of a Circle Point of Tangency Tangent Radius Chord Diameter Communicating About CirclesParts of a CirclePoint of TangencyTangentRadiusChordDiameterSecant
4Communicating About Circles Tell whether each segment is best described as a chord, secant, tangent, diameter, or radiusASecantRadiusChordDiameter
5Communicating About Circles In a plane, two circles can intersect in two points, one point, or no points.One PointTwo PointsCoplanar Circles that intersect in one point are called Tangent CirclesNo Point
6Communicating About Circles Tangent CirclesA line tangent to two coplanar circles is called a Common Tangent
7Communicating About Circles Concentric CirclesTwo or more coplanar circles that share the same center.
8Common External Tangents Communicating About CirclesCommon External TangentsCommon Internal TangentsCommon 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.
9Interior Exterior On the circle Communicating About CirclesA circle divides a plane into three partsInteriorExteriorOn the circle
10External Tell whether the common tangent, CB is Internal or External. Communicating About CirclesTell whether the common tangent, CB is Internal or External.CExternal
11Communicating About Circles Find the center and radius of each circle. Describe the intersection of the two circles and describe all common tangents.Center G: (2, 2)Radius = 2Center H: (6, 2)Common tangents:x = 4; y = 4; and y = 0
12Radius to a Tangent Conjecture Using Properties of TangentsRadius to a Tangent ConjectureIf a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.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.
13Is TS tangent to R? Explain Using Properties of TangentsIs TS tangent to R? ExplainIf the Pythagorean Theorem works then the triangle is a right triangle TS is tangent??NO!
14Using 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 feetTower
15Tangent Segments Conjecture Using Properties of TangentsTangent Segments ConjectureIf two segments from the same exterior point are tangent to the circle, then they are congruent.
16is tangent to R at S. is tangent to R at V. Using Properties of Tangentsis tangent to R at S is tangent to R at V.Find the value of x.x2 - 4
17Find the values of x, y, and z. Using Properties of TangentsFind the values of x, y, and z.All radii are =y = 15Tangent segments are =z = 36