a.) what kind of line ZB intersects the smaller circle a secant or tangent b.) if tangent name the point of tangencyc.) write the equation of this line The image consists of a graph with two circles depicted on the Cartesian plane. Below is a detailed description and transcription suitable for an educational website.---### Cartesian Plane with Two Circles#### Description of the Graph- **Axes:** The graph features the $ x $-axis and $ y $-axis intersecting at the origin $(0,0)$.- **Grid:** The plane is divided into a grid with each line representing integer values along both axes.#### Features on the Graph1. **Large Circle:** - **Center:** Point $ P $. - **Coordinates of $ P $:** $(-2, 1)$. - **Radius:** 3 units. - The circle passes through the points $(-5, 1)$, $(-2, 4)$, and $(-2, -2)$, where each of these points is 3 units away from $ P $.2. **Small Circle:** - **Center:** Point $ Z $. - **Coordinates of $ Z $:** $ (2, -3)$. - **Radius:** 1 unit. - The circle touches the points $(2, -4)$, $(1, -3)$, $(3, -3)$, and $(2, -2)$.#### Labels on the Graph- **Points:** - Point $ A $ is labeled on the negative side of the $ x $-axis (approximately at $-5,0$). - Point $ B $ is labeled on the positive side of the $ x $-axis (at $5,0$). - Point $ C $ is labeled on the positive side of the $ y $-axis (at $0,5$).- **Axes:** - Arrows are drawn at the ends of both axes indicating the positive and negative directions.This graph effectively demonstrates the relationship between circle geometry and the Cartesian coordinate system. The centers of both circles are identified and their respective radii allow for visualization of key concepts in coordinate geometry.

To write the name of the line ZB that intersects the smaller circle

Answered: -2 -1 -2 -4

Math

Geometry

-2 -1 -2 -4

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

a.) what kind of line ZB intersects the smaller circle a secant or tangent b.) if tangent name the point of tangency c.) write the equation of this line

The image consists of a graph with two circles depicted on the Cartesian plane. Below is a detailed description and transcription suitable for an educational website.

---

### Cartesian Plane with Two Circles

#### Description of the Graph

- **Axes:** The graph features the $ x $-axis and $ y $-axis intersecting at the origin $(0,0)$.
- **Grid:** The plane is divided into a grid with each line representing integer values along both axes.

#### Features on the Graph

1. **Large Circle:**
- **Center:** Point $ P $.
- **Coordinates of $ P $:** $(-2, 1)$.
- **Radius:** 3 units.
- The circle passes through the points $(-5, 1)$, $(-2, 4)$, and $(-2, -2)$, where each of these points is 3 units away from $ P $.

2. **Small Circle:**
- **Center:** Point $ Z $.
- **Coordinates of $ Z $:** $ (2, -3)$.
- **Radius:** 1 unit.
- The circle touches the points $(2, -4)$, $(1, -3)$, $(3, -3)$, and $(2, -2)$.

#### Labels on the Graph

- **Points:**
- Point $ A $ is labeled on the negative side of the $ x $-axis (approximately at $-5,0$).
- Point $ B $ is labeled on the positive side of the $ x $-axis (at $5,0$).
- Point $ C $ is labeled on the positive side of the $ y $-axis (at $0,5$).

- **Axes:**
- Arrows are drawn at the ends of both axes indicating the positive and negative directions.

This graph effectively demonstrates the relationship between circle geometry and the Cartesian coordinate system. The centers of both circles are identified and their respective radii allow for visualization of key concepts in coordinate geometry.

Two-dimensional figure measured in terms of radius. It is formed by a set of points that are at a constant or fixed distance from a fixed point in the center of the plane. The parts of the circle are circumference, radius, diameter, chord, tangent, secant, arc of a circle, and segment in a circle.

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