Sect. 10.1 Tangents to Circles Goal 1 Communicating About Circles Goal 2 Using Properties of Tangents

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

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

Communicating About Circles Example 1: Tell whether each segment is best described as a chord, secant, tangent, diameter, or radius A Secant Radius Chord Diameter

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

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

Communicating About Circles 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 is Internal or External. Communicating About Circles Example 2: Tell whether the common tangent is Internal or External. External

Common tangents: x = 4; y = 4; and y = 0 Communicating About Circles Example 3: 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 Theorem 10.1 and 10.2 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 Example 4: Is TS tangent to R? Explain

Using Properties of Tangents Example 5: 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

Using Properties of Tangents Theorem 10.3 If two segments from the same exterior point are tangent to the circle, then they are congruent.

Using Properties of Tangents Example 6: is tangent to R at S. is tangent to R at V. Find the value of x. x2 - 4 x = 5 or -5

Using Properties of Tangents Example 7: is tangent to R at S. is tangent to R at V. Find the value of x. x2 + 8 x = 6 or -6

x = 39 y = 15 z = 36 Find the values of x, y, and z in the diagram. Using Properties of Tangents Example 8: Find the values of x, y, and z in the diagram. x = 39 y = 15 z = 36