Chapter 14: Circle Segment Relationships Topic 1: Segment Theorem ...

[Pages:4]Name: ______________________________________________________________ Date: ______________________ Period: ______ Chapter 14: Circle Segment Relationships Topic 1: Segment Theorem - Chords

Theorem 1: If two chords intersect in a circle, the product of the lengths of the segments of one chord equal the product of the segments of the other

Intersecting Chords Rule: (segment piece)?(segment piece) = (segment piece)?(segment piece)

1. Given: circle with two chords as marked, find x 2. Find x.

3. Find x.

4. Find x.

5. Find x.

7. Find: x = ________ EB = ________ AB = ________ CD = ________

6. Find x.

8.) In the circle shown, DE = 11, BC = 10, and DF = 8. FC > FB. Find FE, BF, and FC.

9.) In the given circle, DE = x, BE = x + 2, AE = 8, and EC = 12. Find the length of chords AB and DC.

10.) Chords AB and CD intersect at point E in a circle with center at O. If AE = 8, AB = 20, and DE = 16, what is

the length of CE?

(1) 6

(2) 9

(3) 10

(4) 12

11.) In the circle shown, DE = 18, BC = 12, and DF = 2. BF < FC. Find FE, BF, and FC.

Name: ______________________________________________________________ Date: ______________________ Period: ______

Segment Theorem - Chords HOMEWORK

Complete the following questions. Show all work, when necessary.

1.) In the diagram of circle O below, chord intersects chord at E, DE = 2x + 8, EC = 3, AE = 4x ? 3, and EB = 4. What is the value of x?

(1) 1

(2) 3.6

(3) 5

(4) 10.25

2.) In the diagram below of circle O, chords and intersect at E. If CE = 10, ED = 6, and AE = 4, what is the length of EB?

(1) 15

(2) 12

(3) 6.7

(4) 2.4

3.) In the diagram below of circle O, chord bisects chord at E. If AE = 8 and BE = 9, find the length of in simplest radical form.

4.) A toy truck is located within a circular play area. Chris and Rebecca are sitting on opposite endpoints of a chord that contains the truck. Chris is 4 feet from the truck, and Rebecca is 3 feet from the truck. Alexis and Preston are sitting on opposite ends of another chord containing the truck. Alexis is 8 feet from the truck. How many feet, to the nearest tenth of a foot, is Preston from the truck? Draw a diagram to support your answer.

5.) In the accompanying diagram of circle O, chords and intersect at E. If AE = 3, EB = 4, CE = x, and ED = x ? 4, what is the length of chord ?

Review Questions

6.) If the area of a square garden is 48 square feet, what is the length, in feet, of one side of the garden?

(1) 122

(2) 43

(3) 163

(4) 46

7.) If x = -2 and y = -1, which point on the accompanying set of axes represents the translation (x,y) (x + 2, y ? 3)?

(1) Q

(2) R

(3) S

(4) T

8.) An image of a building in a photograph is 6 centimeters wide and 11 centimeters tall. If the image is similar to the actual building and the actual building is 174 meters wide, how tall is actual building in meters?

9.) Which statement is false? (1) All parallelograms are quadrilaterals. (2) All rectangles are parallelograms. (3) All squares are rectangles. (4) All rhombuses are squares.

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