Tangents Sec: 12.1 Sol: G.11a,b

A line is ______________________ to a circle if it intersects the circle in exactly one point. This point is called the point of _______________________________.

Consider the following diagram:

Example: If RT is tangent to Circle O, Then OR  RT

The converse of the last theorem is also true. This means: 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. If OR  RT, RT is tangent to Circle O

If a line is tangent to a circle, then it is ________________________________ to the radius drawn to the point of tangency. Example:

Example:

Theorem 10.11: If two __________from the same exterior point are tangent to a circle, then the two segments are ______. Example: AB  CB

117° X°

Example x+4 y 10 y-5

Circumscribed polygons: A polygon is circumscribed about a circle if each side of the polygon is tangent to the circle. ◦ Example:

Example: Triangle HJK is circumscribed about circle G. Find the Perimeter of HJK if NK = JL JL + 29

Arcs and Chords Sec: 12.2 Sol: G.11a,b

Recall the definitions of minor arcs & chords (draw an example of each on  A below): Example: When minor arc and a chord share the same endpoints, we call the arc the arc of the chord. Example:

In a circle or in congruent circles, two __________ ________ are congruent if and only if their corresponding chords are congruent. Example: In  A, if, then ____  ____.

In a circle, if a diameter is perpendicular to a chord, then it bisects the chord and its arc. Example:

In a circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center. Example:

Find x in each problem Suppose a chord of a circle is 10 inches long and is 12 inches from the center of the circle. Find the length of the diameter. 3. Suppose the diameter of a circle is 34 inches long and a chord is 30 inches long. Find the distance between the chord and the center of the circle. 4. Suppose a chord of a circle is 24 cm long and is 15 cm from the center of the circle. Find the length of the radius.

Suggested Assignments Classwork: Handouts Homework: Pg ,12-18even,19,26 and Pg Even, 13-16,30