Tangent Line -

a line that touches a circle at only one point

Point of Tangency -

the point where a tangent and a circle intersect

Section 12.2 - Chords and Arcs

Chord -

a segment whose endpoints are both on the circle

Section 12.3 - Inscribed Angles

Inscribed Angle -

an angle whose vertex is on the circle and whose sides are chords of the circle.

Intercepted Arc -

an arc created by the endpoints of an inscribed angle

Section 12.4 - Angle Measures and Segment Lengths

Angles formed by intersecting lines have a special relationship to the related arcs formed when the lines intersect a circle.

Secant -

a line that intersects a circle at two points

**Chapter 12**

**Circles**

AB

is a tangent line

B

is the point of tangency

Theorem 12.1 - Tangency to a Circle

If a line is tangent to a circle, then the line is perpendicular to the radius at the point of tangency.

AB

is tangent to circle O

AB OP

T

Solve for x. Assume all lines that appear to be tangent are tangent.

Solve for x. Assume all lines that appear to be tangent are tangent.

Theorem 12.2 - Converse of Tangency to a Circle

If a line in the plane of a circle is perpendicular to the radius at its endpoint on the circle, then the line is tangent to the circle.

AB

must be tangent to circle O

What value of x makes AB tangent to circle C?

Theorem 12.3 - Tangents Meeting Outside a Circle

If two tangent segments to a circle share a common endpoint outside the circle, then the two segments are congruent.

AB = BC

~

Find the perimeter of triangle ABC.

Homework #29 - Section 12.1

Complete in Math XL

Remember!!! You must complete 100% of the assignment in order to earn full credit in the grade book.

Theorem 12.4 - Central Angles and Arcs

Within a circle or in congruent circles, congruent central angles have congruent arcs.

Within a circle or in congruent circles, congruent arcs have congruent central angles.

Theorem 12.5 - Angles and Chords

Within a circle or in congruent circles, congruent central angles have congruent chords.

Within a circle or in congruent circles, congruent chords have congruent central angles.

Theorem 12.6 - Chords and Arcs

Within a circle or in congruent circles, congruent chords have congruent arcs.

Within a circle or in congruent circles, congruent arcs have congruent chords.

Theorem 12.7 - Chords and the Center of a Circle

Within a circle or in congruent circles, chords equidistant from the center are congruent.

Within a circle or in congruent circles, congruent chords are equidistant from the center.

Theorem 12.8 - Diameters and Chords

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

Theorem 12.9 - Converse of 12.8

In a circle, if a diameter bisects a chord, then it is perpendicular to the chord.

Theorem 12.10 - Perpendicular Bisectors in Circles

In a circle, the perpendicular bisector of a chord contains the center of the circle (diameter).

Solve for x

Solve for x

Solve for x

Find the measure of AB

Homework #30 - Section 12.2

Complete in Math XL

Remember!!! You must complete 100% of the assignment in order to earn full credit in the grade book.

Theorem 12.11 - Inscribed Angle Theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Solve for each variable

Solve for each variable

Solve for each variable

Corollaries to Theorem 12.11

Theorem 12.12 - Tangents and Chords

The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.

Solve for each variable

Solve for each variable

Solve for each variable

Homework #31 - Section 12.3

Complete in Math XL

Remember!!! You must complete 100% of the assignment in order to earn full credit in the grade book.

Theorem 12.13 - Angles Inside Circles

The measure of an angle formed by two lines that intersect inside a circle is half the sum of the measures of the intercepted arcs.

Theorem 12.14 - Angles Outside Circles

The measure of an angle formed by two lines that intersect outside a circle is half the difference of the intercepted arcs.

Solve for x

Solve for x

Theorem 12.15 - Circles and Segments

For a given point and circle, the product of the lengths of the two segments from the point to the circle is constant along any line through the point and circle.

(two chords) (two secants) (tangent and secant)

Solve for x

Solve for c

Solve for each variable

Homework #32 - Section 12.4

Complete in Math XL

Remember!!! You must complete 100% of the assignment in order to earn full credit in the grade book.