Warm-Up #33 3. Find x. 1. What is the perimeter of a regular hexagon if one of the side is 10 inches. 2. Find x X = 36 degrees Perimeter = 60 units X = 135 degrees

Warm-up #34

Homework Tangent Lines

Tangents to Circles

If two circles have the same radius, then the circles are congruent Congruent circles

Definition of Concentric Circles Concentric circles have the same center, just with different radii on the same plane.

Diagram of Important Terms center

Definition of Chords A chord is a line segment the touches the edges of the inside of a circle. The Greatest Chord is the longest Chord in a circle, called the diameter.

Definition of a Secant A secant is a line touching the circle at two points

Definition of a Tangent A line or line segment touching the circle at one point.

Common Tangents Interior common tangents would go through a line segment drawn from the centers of two circles.

Common Tangents Exterior common tangents do not cross a segment between the center of two circles

What is it?

Point of Tangency Theorem If a line is tangent to a circle, then it makes a right angle to the radius at the point of tangency.

Point of Tangency Theorem (Converse) If a line is perpendicular to the radius at its endpoint, then the line is tangent to the circle

Find the radius of the circle What do you notice about the shape created by the lines? It’s a right triangle, so we’ll use the Pythagorean theorem. x 12 13

Theorem about the Intersection of two tangent line segment If two tangent lines intersect at one point, the segments from the point to the point of tangency are congruent.

Find the value for the variable

Find the value for the variable 14 x 4

Solve for x The line segment are tangent to the circle

Solve for y The line segment are tangent to the circle

Find x

Which sides are congruent? 3x2+ 15 = 2x2 +79 3x2 + 15 x2 + 15 = 79 x2 = 64 x = 8 2x2 + 79

Find the value of x 4x2 – 5x 3 - 4x