12.4 Segment Lengths in Circles. Finding the Lengths of Chords When two chords intersect in the interior of a circle, each chord is divided into two segments.

Slides:

Advertisements

Similar presentations

Bellwork 1) (x+3)(x+7) 2) (2x+4)(x-4).

Advertisements

10.1 Tangents to Circles.

The Power Theorems Lesson 10.8

Geometry Honors Section 9.5 Segments of Tangents, Secants and Chords.

Tangency. Lines of Circles EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord,

Section 12.1: Lines That intersect Circles

Other Angle Relationships

Bellwork  If 10 is multiplied by 10 more than a number, the product is the square of 24. Find the number  Solve for x 21(x-4)=(2x-7)(x+2) 3x 2 -13x-7=0.

Special Segments in a Circle Find measures of segments that intersect in the interior of a circle. Find measures of segments that intersect in the exterior.

10.5: Find Segment Lengths in Circles

Lesson 8-6: Segment Formulas

10.5 Segment Lengths in Circles Geometry Mrs. Spitz Spring 2005.

9.7 Segment Lengths in Circles

Warm-Up 7. Find the value of x and y. 8. Find the measure of arc AC.

1 Lesson 10.6 Segment Formulas. 2 Intersecting Chords Theorem A B C D E Interior segments are formed by two intersecting chords. If two chords intersect.

LESSON F: Segment Lengths in Circles During this lesson, you will find the lengths of segments of chords, tangents and secants in circles.

Lines That Intersect Circles

12.4 Other Angle Relationships in Circles

Properties of Tangents. EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord, diameter,

EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent.

Finding Lengths of Segments in Chords When two chords intersect in the interior of a circle, each chord is divided into two segments which are called segments.

EXAMPLE 3 Find lengths using Theorem Use the figure at the right to find RS. SOLUTION 256= x 2 + 8x 0= x 2 + 8x – 256 RQ 2 = RS RT 16 2 = x (x +

10.5 Segment Lengths in Circles

11.4 angle measures and segment lengths

10.6 Segment Lengths in Circles

W ARM - UP : S OLVE IN YOUR NOTEBOOK 1. 8x = (10+8)=6(y+6) =6(2x+8) =x(x+6)

Other Angle Relationships in Circles

6.6 Find Segment Lengths in Circles Quiz: MONDAY! Quiz: Nov Test: Nov. 30 Performance Exam: Dec. 2.

10.5 Segment Lengths in Circles Geometry. Objectives/Assignment Find the lengths of segments of chords. Find the lengths of segments of tangents and secants.

Find Segment Lengths in Circles Lesson Definition When two chords intersect in the interior of a circle, each chord is divided into two segments.

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.

Warm - up Segment Lengths in Circles Section 6.6.

10.1 Tangents to Circles. Some definitions you need Circle – set of all points in a plane that are equidistant from a given point called a center of the.

10-6 Find Segment Lengths in Circles. Segments of Chords Theorem m n p m n = p q If two chords intersect in the interior of a circle, then the product.

Rules for Dealing with Chords, Secants, Tangents in Circles

10.5 Segment Lengths in Circles

Find Segment Lengths in Circles

Segment Lengths Geometry 11-4b.

10.5 Chord Length When two chords intersect in the interior of a circle, each chord is divided into segments. Theorem: If two chords intersect in the interior.

Find Segment Lengths in Circles

10.5 Segment Lengths in Circles

DRILL Solve for x: 220° (2x+ 5)° 100°.

Section 10.6 Segments in Circles.

Segment Lengths in Circles

Module 19: Lesson 4 Segment Relationships in Circles

Solve the equation. 1. x2 + 4x + 3 = x – 9 = x2 ANSWER –1, –3

Lines that Intersect Circles

Lesson 8-6: Segment Formulas

Lesson 15.4 Materials: Notes Textbook.

10-7 Special Segments in a Circle

Lesson 8-6: Segment Formulas

10.1 Tangents to Circles.

10.5 Segment Lengths in Circles

Objectives Identify tangents, secants, and chords.

Segments of Chords, Secants & Tangents Lesson 12.7

Segment Lengths in Circles

Aim: How do we find the length of secants?

Lesson 8-6: Segment Formulas

Segment Lengths in Circles

Lesson 8-6 Segment Formulas.

Unit 3: Circles & Spheres

Lesson 10-7: Segment Formulas

LESSON LESSON PART I ANGLE MEASURES

6.6 Finding Segment Lengths.

Segment Lengths in Circles

Essential Question Standard: 21 What are some properties of

Segment Lengths in Circles

Whole Sheet Chord-Chord Secant-Tangent Secant-Secant Tangent-Tangent.

Presentation transcript:

12.4 Segment Lengths in Circles

Finding the Lengths of Chords When two chords intersect in the interior of a circle, each chord is divided into two segments which are called segments of a chord. The following theorem gives a relationship between the lengths of the four segments that are formed.

Theorem (I) If two chords intersect in the interior of a circle, then 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 chord. EA EB = EC ED

Ex. 1: Finding Segment Lengths Chords ST and PQ intersect inside the circle. Find the value of x. RQ RP = RS RTUse Theorem Substitute values.9 x = 3 6 9x = 18 x = 2 Simplify. Divide each side by 9.

Theorem (II) If two secant segments share the same endpoint outside a circle, then the product of the length of one secant segment and the length of its external segment equals the product of the length of the other secant segment and the length of its external segment. EA EB = EC ED

Theorem (III) If a secant segment and a tangent segment share an endpoint outside a circle, then the product of the length of the secant segment and the length of its external segment equal the square of the length of the tangent segment. (EA) 2 = EC ED

Ex. 2: Finding Segment Lengths Find the value of x. RP RQ = RS RTUse Theorem Substitute values.9(11 + 9)=10(x + 10) 180 = 10x = 10x Simplify. Subtract 100 from each side. 8 = x Divide each side by 10.

Ex. 3: Estimating the radius of a circle Aquarium Tank. You are standing at point C, about 8 feet from a circular aquarium tank. The distance from you to a point of tangency is about 20 feet. Estimate the radius of the tank.

(CB) 2 = CE CDUse Theorem Substitute values. 400  16r  16r Simplify. 21  r Divide each side by 16. (20) 2  8 (2r + 8) Subtract 64 from each side.  So, the radius of the tank is about 21 feet.

(BA) 2 = BC BDUse Theorem Substitute values. 25 = x 2 + 4x 0 = x 2 + 4x - 25 Simplify. Use Quadratic Formula. (5) 2 = x (x + 4) Write in standard form. x =Simplify. Use the positive solution because lengths cannot be negative. So, x = -2 +  x =

Homework Page # 9-14, & 38