Copyright © 2014 Pearson Education, Inc.

Slides:

Advertisements

Similar presentations

Other Angle Relationships in Circles Section 10.4

Advertisements

Classifying Angles with Circles

Definitions A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. Radius – the distance.

Tangents, Arcs, and Chords

11.2/11.3 Tangents, Secants, and Chords

CIRCLES 2 Moody Mathematics.

Definitions A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. Radius – the distance.

Circle. Circle Circle Tangent Theorem 11-1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of.

Other Angle Relationships

By Mark Hatem and Maddie Hines

Apply Other Angle Relationships in Circles

Circles Chapter 10.

Geometry Section 10.4 Angles Formed by Secants and Tangents

Tangents to Circles (with Circle Review)

Circles and Chords. Vocabulary A chord is a segment that joins two points of the circle. A diameter is a chord that contains the center of the circle.

M—06/01/09—HW #75: Pg : 1-20, skip 9, 16. Pg : 16—38 even, 39— 45 odd 2) C4) B6) C8) A10) 512) EF = 40, FG = 50, EH = ) (3\2, 2); (5\2)18)

SECANTS Secant - A line that intersects the circle at two points.

Circles Chapter 9. Tangent Lines (9-1) A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point. The.

Circles Chapter 12.

Section 10.1 Theorem 74- If a radius is perpendicular to a chord, then it bisects the chord Theorem 74- If a radius is perpendicular to a chord, then it.

12.2 Chords and Arcs Theorem 12.4 and Its Converse Theorem –

11-2 Chords and Arcs  Theorems: 11-4, 11-5, 11-6, 11-7, 11-8  Vocabulary: Chord.

6.5Apply Other Angle Relationships Theorem 6.13 If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one.

$ $ $ $ $ 100 $ $ $ $ $ $ $ $ $ $ $ 200.

10.3 – Apply Properties of Chords. In the same circle, or in congruent circles, two ___________ arcs are congruent iff their corresponding __________.

Going Around in Circles!

Chord and Tangent Properties. Chord Properties C1: Congruent chords in a circle determine congruent central angles. ●

Inscribed Angles December 3, What is an inscribed angle? An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords.

Section 10.5 Angles in Circles.

6.5 Other Angle Relationships in Circles. Theorem 6.13 If a tangent and a chord intersect at a point on the circle, then the measure of each angle formed.

Geometry Warm-Up4/5/11 1)Find x.2) Determine whether QR is a tangent.

Section 9-7 Circles and Lengths of Segments. Theorem 9-11 When two chords intersect inside a circle, the product of the segments of one chord equals the.

Section 10-2 Arcs and Central Angles. Theorem 10-4 In the same circle or in congruent circles, two minor arcs are congruent if and only if their corresponding.

PROPERTIES OF CIRCLES Chapter – Use Properties of Tangents Circle Set of all points in a plan that are equidistant from a given point called.

Circle Geometry.

Objectives: To use the relationship between a radius and a tangent To use the relationship between two tangents from one point.

Chapter 7 Circles. Circle – the set of all points in a plane at a given distance from a given point in the plane. Named by the center. Radius – a segment.

12.2 Chords and Arcs.

10.3 – Apply Properties of Chords

Do Now 1.) Explain the difference between a chord and a secant.

Section 10.4 Arcs and Chords.

Other Angle Relationships in Circles

Tangent of a Circle Theorem

Geometry 11.4 Color Theory.

Copyright © 2014 Pearson Education, Inc.

Section 10.5 Angles in Circles.

11.4 Angle Measures and Segment Lengths

12-4 Angle Measures and Segment Lengths

Chords, secants and tangents

Other Angle Relationships in Circles

Do Now One-half of the measure of an angle plus the angle’s supplement is equal to the measure of the angle. Find the measure of the angle.

12.1 Tangent lines -Theroem 12.1: if a line is tangent to a circle, then it will be perpendicular to the radius at the point of tangency -Theroem 12.3:

Chapter 10.5 Notes: Apply Other Angle Relationships in Circles

Section 11 – 2 Chords & Arcs Objectives:

9-6 Other Angles.

Section 6.3: Line and Segment Relationships in the Circle.

Angles Related to a Circle

Apply Other Angle Relationships

Secants, Tangents, and Angle Measure

Section 10.4 – Other Angle Relationships in Circles

Angles Related to a Circle

Chapter 9 Section-6 Angles Other.

Segment Lengths in Circles

Y. Davis Geometry Notes Chapter 10.

12.2 Chords & Arcs.

Chapter 9-4 Arcs and Chords.

Presentation transcript:

Copyright © 2014 Pearson Education, Inc. 6 CHAPTER 6.2 Chords and Secants Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Chords Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Theorem 6.5 When two chords of circle intersect, the measure of each angle formed is one-half the sum of the measures of its intercepted arc and the arc intercepted by its vertical angle. Copyright © 2014 Pearson Education, Inc.

Finding Angle Measures a. What is the value of the variable? Solution The lines intersect inside the circle, so we find half the addition of arcs. Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. More Theorems Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Bisector of an Arc A line that divides and arc into two arcs with the same measure is called a bisector of the arc. Copyright © 2014 Pearson Education, Inc.

Perpendicular Line Theorems Thm 6.8 – A line drawn from the center of a circle perpendicular to a chord bisects the chord and the arc formed by the chord. Thm 6.9 – A line drawn from the center of a circle to the midpoint of a chord (not a diameter) or to the midpoint of the arc formed by the chord is perpendicular to the chord. Copyright © 2014 Pearson Education, Inc.

Congruent Chord Theorems Thm 6.10 – In the same circle, congruent chords are equidistant from the center of the circle. Thm 6.11- In the same circle, chords equidistant from the center of the circle are congruent. Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. More Theorems Thm 6.12 – The perpendicular bisector of a chord passes through the center of the circle. Thm 6.13 – If two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other. Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Definition A secant is a line that intersects a circle at two points. Copyright © 2014 Pearson Education, Inc.

Theorem 6.14 Secants Intersecting Outside a Circle If two secants intersect forming an angle outside the circle, then the measure of this angle is one-half the difference of the measures of the intercepted arcs. Copyright © 2014 Pearson Education, Inc.

Finding Angle Measures b. What is the value of the variable? Solution The lines intersect outside the circle, so we find half the difference of arcs. Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Finding an Arc Measure A satellite in a geostationary orbit above Earth’s equator has a viewing angle of Earth formed by the two tangents to the equator. The viewing angle is about 17.5°. What is the measure of the arc of Earth that is viewed from the satellite? Solution The sum of the measures of the arcs of a circle is 360°. Let Copyright © 2014 Pearson Education, Inc.

Copyright © 2014 Pearson Education, Inc. Finding an Arc Measure Copyright © 2014 Pearson Education, Inc.

Theorem 6.15 Segment Products—Inside or Outside a Circle Copyright © 2014 Pearson Education, Inc.

Finding Segment Lengths Find the value of the variable in the circle. Solution 6(6 + 8) = 7(7 + y) 6(14) = 7(7 + y) 84 = 49 + 7y 35 = 7y 5 = y Copyright © 2014 Pearson Education, Inc.

Finding Segment Lengths Find the value of the variable in the circle. Solution 8(8 + 16) = z2 8(24) = z2 192 = z2 13.9 ≈ z Copyright © 2014 Pearson Education, Inc.