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# Chapter 12

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by

## Josh Truax

on 7 May 2018

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#### Transcript of Chapter 12

Section 12.1 - Tangent Lines
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 #27 - 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 #28 - 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 #29 - 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 #30 - 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.
Notebook Question #1
Notebook Question #2
Notebook Question #3
Notebook Question #4
Notebook Question #1
Notebook Question #2
Notebook Question #3
Notebook Question #4
Notebook Question #1
Notebook Question #2
Notebook Question #3
Notebook Question #4
Notebook Question #5
Notebook Question #6
Notebook Question #1
Notebook Question #2
Notebook Question #3
Notebook Question #4
Notebook Question #5
Full transcript