https://file.aiquickdraw.com/mathbot/file/1724666133330v0k6p1hu.jpg

the topic is tangent lines, what is the perimeter of the red polygon

To find the perimeter of the red polygon, let's break down the information given in the image:

### Step 1: Analyze the Given Data
- The red polygon is a quadrilateral, with side lengths labeled as 2 cm, 3 cm, 4 cm, and 4 cm.
- The yellow circle is inscribed in the red quadrilateral, meaning it is tangent to all four sides.

### Step 2: Use the Tangent-Segment Theorem
For a quadrilateral inscribed in a circle (tangential quadrilateral), the sum of the lengths of the opposite sides is equal. This property will help in verifying the perimeter calculation.

Given the side lengths:
- Two opposite sides are 4 cm each.
- The other two sides are 2 cm and 3 cm.

### Step 3: Calculate the Perimeter
Add up all the sides:
\[
\text{Perimeter} = 2\,\text{cm} + 3\,\text{cm} + 4\,\text{cm} + 4\,\text{cm} = 13\,\text{cm}
\]

### Final Answer:
The perimeter of the red polygon is **13 cm**.

Would you like more details on the tangent-segment theorem, or do you have any other questions?

---

Here are 5 related questions to explore further:
1. How does the tangent-segment theorem apply to other shapes besides quadrilaterals?
2. What are the conditions for a quadrilateral to have an inscribed circle?
3. How would the problem change if the quadrilateral were not tangential?
4. What is the relationship between the area of the quadrilateral and the radius of the inscribed circle?
5. How would you find the area of the red polygon?

**Tip:** Always verify if a quadrilateral is tangential before applying properties specific to tangential quadrilaterals!

Learn how to calculate the perimeter of a red polygon using the tangent-segment theorem. This problem involves analyzing a quadrilateral with specified side lengths and understanding the properties of tangent quadrilaterals. Suitable for Grades 7-9 students studying geometry and polygons.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation