SECTION 10.6 – SECANTS, TANGENTS AND ANGLE MEASURES

SECANTS, TANGENTS AND ANGLE MEASURES

How do I find the measures of angle formed by lines intersecting on or inside a circle?

How do I find the measures of angles formed by lines intersecting outside the circle?

SECANT

Secant: A line that intersects a circle in exactly 2 points.

SECANTS VS. TANGENTS

Know the difference!

THEOREM

Theorem 10.12: If two secants intersect in the interior of a circle, then the measure of the angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

THEOREM

Theorem 10.13: If a secant and a tangent intersect at the point of tangency, then the measure of each angle formed is one-half the measure of the intercepted arc.

THEOREM

Theorem 10.14: If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

THEOREM 10.14

Two secants

THEOREM 10.14

A secant and a tangent

THEOREM 10.14

Two tangents meeting outside the circle

EXAMPLE

Find if and = 76.

F

G

HE

4

3

88°

76°

EXAMPLE

Find if and = 136.

Q

P

R

S

T

114°

136°

EXAMPLE

Find x.

6x°40°

55°

EXAMPLE

A jeweler wants to craft a pendant with the shape shown. Use the figure to determine the measure of the arc at the bottom of the pendant.

40°

HOMEWORK

Page 564 #3 – 7 12 - 32

LESSON PLAN

Intro Define a secant. Define secant and tangents

relationships to a circle’s arcs Standards- 9.6 Supplies – slides, whiteboard, note sheets Timing: One day for notes, one day for a

combined review of 10.5, 10.6 and 10.8, followed by a quiz.

Day 1: Essential Questions- slides 2 Input-slides 3 - 7 Guided Practice - slides 8 - 15 Independent Practice – Book Work