**In Exercises 3–6, find the value of x. (See Example 1.)****3.**A circle is divided by two intersecting chords, creating four segments with labeled lengths. The lengths of these segments are:- 10 units- 12 units- 6 units- x units**5.**Another circle is divided by two intersecting chords, creating four segments with labeled lengths. The lengths of these segments are:- x units- 8 units- x + 8 units- 6 unitsTo solve for x in these types of problems, use the intersecting chords theorem, which states that the product of the lengths of the two segments of one chord equals the product of the lengths of the two segments of the other chord. For example:If $ AB $ and $ CD \ ) are two chords intersecting inside the circle at point \( E $, then $ AE \cdot EB = CE \cdot ED $.

Name: **In Exercises 3–6, find the value of x. (See Example 1.)****3.**A ci
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Description: **In Exercises 3–6, find the value of x. (See Example 1.)****3.**A circle is divided by two intersecting chords, creating four segments with labeled lengths. The lengths of these segments are:- 10 units- 12 units- 6 units- x units**5.**Another circl

From the figure, 12 . x = 10 . 6 x = 60 / 12 x = 5

Answered: 3. 8, 12 10 x + 8 LO 5.

Math

Geometry

3. 8, 12 10 x + 8 LO 5.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Concept explainers

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.

Topic Video

Question

**In Exercises 3–6, find the value of x. (See Example 1.)**

**3.**
A circle is divided by two intersecting chords, creating four segments with labeled lengths. The lengths of these segments are:
- 10 units
- 12 units
- 6 units
- x units

**5.**
Another circle is divided by two intersecting chords, creating four segments with labeled lengths. The lengths of these segments are:
- x units
- 8 units
- x + 8 units
- 6 units

To solve for x in these types of problems, use the intersecting chords theorem, which states that the product of the lengths of the two segments of one chord equals the product of the lengths of the two segments of the other chord.

For example:
If $ AB $ and $ CD \ ) are two chords intersecting inside the circle at point \( E $, then $ AE \cdot EB = CE \cdot ED $.

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