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Lesson 6.1 Tangents to Circles

Lesson 6.1 Tangents to Circles. Goal 1 Communicating About Circles Goal 2 Using Properties of Tangents. Communicating About Circles. Circle Terminology:.

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Lesson 6.1 Tangents to Circles

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

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

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

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

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

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

  7. Communicating About Circles Common External Tangents Common Internal 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.

  8. Communicating About Circles A circle divides a plane into three parts • Interior • Exterior • On the circle

  9. Using Properties of Tangents Radius to a Tangent Conjecture If 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.

  10. 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!

  11. 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

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

  13. Using Properties of Tangents is tangent to R at S. is tangent to R at V. Find the value of x. x2 - 4

  14. 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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