 Lesson 6.1 Tangents to Circles

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

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

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

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

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

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

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

Common External Tangents
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.

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

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

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 = 2 Center H: (6, 2) Common tangents: x = 4; y = 4; and y = 0

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.

Is TS tangent to R? Explain
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!

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

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

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

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