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7. Angle QRS is circumscribed about circle P. If QR = 24x ft and RS= 4x + 5 ft, what is the length of RS in feet? 24x Ś 4x +5 R

7. Angle QRS is circumscribed about circle P. If QR = 24x ft and RS= 4x + 5 ft, what is the length of RS in feet? 24x Ś 4x +5 R

Elementary Geometry For College Students, 7e
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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Answer question 7

### Question 7: **Angle QRS is circumscribed about circle P.** Given: - \( QR = 24x \) ft - \( RS = 4x + 5 \) ft **Problem:** What is the length of \( \overline{RS} \) in feet? **Explanation:** The diagram consists of a triangle \( \triangle QRS \) circumscribed about a circle with center \( P \). Two sides of the triangle, \( QR \) and \( RS \), have lengths given in terms of the variable \( x \): - \( QR = 24x \) - \( RS = 4x + 5 \) The illustration shows a circle touching the sides of the triangle at three points, illustrating the properties of a tangential quadrilateral where opposite angles are supplementary. To find the length of \( RS \), we need to determine the value of \( x \) from given or derived information. ### Solution: 1. **Step 1: Set up any necessary equations based on geometric properties of the tangential quadrilateral**. 2. **Step 2: Solve for \( x \)** based on provided relationships. 3. **Step 3: Substitute value of \( x \) back into the expression \( 4x + 5 \) to determine the exact length of \( RS \)**. The problem requires knowledge of geometry particularly dealing with properties of tangential quadrilaterals and algebraic manipulation to solve for \( x \). Encouraged steps: - Determine if there's additional geometric information deriving angle relationships or other side lengths. - Engage algebraic solving once the setup is confirmed.
Transcribed Image Text:### Question 7: **Angle QRS is circumscribed about circle P.** Given: - \( QR = 24x \) ft - \( RS = 4x + 5 \) ft **Problem:** What is the length of \( \overline{RS} \) in feet? **Explanation:** The diagram consists of a triangle \( \triangle QRS \) circumscribed about a circle with center \( P \). Two sides of the triangle, \( QR \) and \( RS \), have lengths given in terms of the variable \( x \): - \( QR = 24x \) - \( RS = 4x + 5 \) The illustration shows a circle touching the sides of the triangle at three points, illustrating the properties of a tangential quadrilateral where opposite angles are supplementary. To find the length of \( RS \), we need to determine the value of \( x \) from given or derived information. ### Solution: 1. **Step 1: Set up any necessary equations based on geometric properties of the tangential quadrilateral**. 2. **Step 2: Solve for \( x \)** based on provided relationships. 3. **Step 3: Substitute value of \( x \) back into the expression \( 4x + 5 \) to determine the exact length of \( RS \)**. The problem requires knowledge of geometry particularly dealing with properties of tangential quadrilaterals and algebraic manipulation to solve for \( x \). Encouraged steps: - Determine if there's additional geometric information deriving angle relationships or other side lengths. - Engage algebraic solving once the setup is confirmed.
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