ARST is shown below. XU = -2y + 15 and XW = 3y + 5. R T S Find the measure of the radius of the inscribed circle of ARST. Enter your answer in the box.

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 14

The image contains a geometrical problem involving a triangle and its inscribed circle. The details and features in the image are explained below:

### Geometry Problem

- **Triangle RST** is shown with vertices labeled **R**, **S**, and **T**.
- In this triangle, there are points labeled **U**, **V**, **W**, and **X** within the triangle and on its sides, helping to highlight certain geometric relationships.
- The lengths involving these points are represented by the equations:
  - **\(XU = -2y + 15\)**
  - **\(XW = 3y + 5\)**

### Diagram Details

- The triangle **RST** is divided by lines extending from the vertices to opposite sides. These lines create smaller triangles within **RST**:
  - **TRU**
  - **RVS**
  - **TWX**
  - **WXS**
  
- Each of these subdivisions suggests angle bisectors or perpendicular lines drawn from vertices, emphasizing relationships that likely involve angle calculations or distance measurements.

### Problem Statement

The problem asks to:
> "Find the measure of the radius of the inscribed circle of **\( \triangle RST \)**. Enter your answer in the box."

### Graphical Explanation

- The diagram helps visualize the relationships between different parts of the triangle and assists in formulation strategies to solve for the radius of the inscribed circle.

### Answer Input

- There is a box provided at the bottom of the graphical problem where the measurement of the radius should be entered.

The task encourages understanding of inscribed circles, angle bisectors, and the application of geometric formulas.
Transcribed Image Text:The image contains a geometrical problem involving a triangle and its inscribed circle. The details and features in the image are explained below: ### Geometry Problem - **Triangle RST** is shown with vertices labeled **R**, **S**, and **T**. - In this triangle, there are points labeled **U**, **V**, **W**, and **X** within the triangle and on its sides, helping to highlight certain geometric relationships. - The lengths involving these points are represented by the equations: - **\(XU = -2y + 15\)** - **\(XW = 3y + 5\)** ### Diagram Details - The triangle **RST** is divided by lines extending from the vertices to opposite sides. These lines create smaller triangles within **RST**: - **TRU** - **RVS** - **TWX** - **WXS** - Each of these subdivisions suggests angle bisectors or perpendicular lines drawn from vertices, emphasizing relationships that likely involve angle calculations or distance measurements. ### Problem Statement The problem asks to: > "Find the measure of the radius of the inscribed circle of **\( \triangle RST \)**. Enter your answer in the box." ### Graphical Explanation - The diagram helps visualize the relationships between different parts of the triangle and assists in formulation strategies to solve for the radius of the inscribed circle. ### Answer Input - There is a box provided at the bottom of the graphical problem where the measurement of the radius should be entered. The task encourages understanding of inscribed circles, angle bisectors, and the application of geometric formulas.
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