Question I & J please ### Transcription of Text and Diagram Explanation**Problems:**1. $ h) \quad AC = 9, \, BC = 5, \, ED = 12, \, CD = ? $2. $ i) \quad ED = 8, \, DC = 4, \, FC = ? $3. $ j) \quad FC = 6, \, ED = 9, \, CD = ? $**Diagram Explanation:**The diagram is a geometric figure that includes a circle with several points labeled around it and extending lines:- The circle has lines $ CA $, $ CB $, and $ CD $ extending from point $ C $ and tangential lines $ CE $ and $ CF $.- A line segment $ ED $ is shown as part of a triangle outside the circle.- A line from $ F $ extends to $ C $, labeled as $ FC $.- Point $ G $ is shown as a point of intersection inside the circle where line segments connect.The problems ask for solving unknown line segments based on the given lengths. These values are likely to be solved using properties of intersecting chords, secants, or tangents related to the circle. Given that $ \overline{CF} $ is a tangent to the circle shown: (Note: In this context, $ \overline{CF} $ refers to the line segment tangent to the circle at a single point, perpendicular to the radius at that point. To understand this better, please refer to a diagram illustrating this tangent line intersecting with the circle.)

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Description: Question I & J please ### Transcription of Text and Diagram Explanation**Problems:**1. $ h) \quad AC = 9, \, BC = 5, \, ED = 12, \, CD = ? $2. $ i) \quad ED = 8, \, DC = 4, \, FC = ? $3. $ j) \quad FC = 6, \, ED = 9, \, CD = ? $**Diagram Explan

Answered: i) ED = 8, DC = 4, FC =? i) FC = 6, ED…

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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Question I & J please

### Transcription of Text and Diagram Explanation

**Problems:**

1. $ h) \quad AC = 9, \, BC = 5, \, ED = 12, \, CD = ? $
2. $ i) \quad ED = 8, \, DC = 4, \, FC = ? $
3. $ j) \quad FC = 6, \, ED = 9, \, CD = ? $

**Diagram Explanation:**

The diagram is a geometric figure that includes a circle with several points labeled around it and extending lines:

- The circle has lines $ CA $, $ CB $, and $ CD $ extending from point $ C $ and tangential lines $ CE $ and $ CF $.
- A line segment $ ED $ is shown as part of a triangle outside the circle.
- A line from $ F $ extends to $ C $, labeled as $ FC $.
- Point $ G $ is shown as a point of intersection inside the circle where line segments connect.

The problems ask for solving unknown line segments based on the given lengths. These values are likely to be solved using properties of intersecting chords, secants, or tangents related to the circle.

Given that $ \overline{CF} $ is a tangent to the circle shown:

(Note: In this context, $ \overline{CF} $ refers to the line segment tangent to the circle at a single point, perpendicular to the radius at that point. To understand this better, please refer to a diagram illustrating this tangent line intersecting with the circle.)

Expert Solution

Step 1

If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

In the circle, $\bar{U V}$ is a tangent and $\bar{U Y}$ is a secant. They intersect at point $U$

Step 2

We have,

(i)

ED=8, and DC=4

So,

$\begin{array}{rcl} C E & = & E D + D C \\ = & 8 + 4 \\ = & 12 \end{array}$

Using Tangent-Secant Theorem,

${(C F)}^{2} = (C D) \cdot (C E) {(C F)}^{2} = (4) \cdot (12) C F = \sqrt{48} C F = 4 \sqrt{3}$

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i) ED = 8, DC = 4, FC =? i) FC = 6, ED = 9, CD =? C D A F