**Exercise 4: Drawing Two Circles with Three Common Tangents**Objective:To understand and illustrate the concept of common tangents between two circles.Instructions:Draw two circles that share exactly three common tangents.Explanation:In geometry, a tangent to a circle is a straight line that touches the circle at exactly one point. Two circles can have up to four common tangents in various configurations. Your task is to draw two circles that have exactly three common tangents.To achieve this:1. **Draw two circles where one is inside the other but does not touch the other.** In this scenario, they share exactly one internal tangent and two external tangents.Here is a step-by-step guide to construct such a figure:1. **Draw the larger circle:** - Use a compass to draw a large circle on your paper. Label the center of this circle as $ O_1 $.2. **Draw the smaller circle inside the larger circle:** - Place the compass at a suitable distance within the boundary of the larger circle and draw a smaller circle. Label the center of this smaller circle as $ O_2 $.3. **Identify the three common tangents:** - Draw the internal tangent: This is the line that touches both circles but stays inside the larger circle. - Draw the two external tangents: These are the lines that touch both circles from the outside.Visual aid:- Ensure the circles do not intersect.- Clearly indicate the tangents.By completing this exercise, you will be able to visualize the geometric relationship between circles and their tangents, and fully understand the concept of common tangents.

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Description: **Exercise 4: Drawing Two Circles with Three Common Tangents**Objective:To understand and illustrate the concept of common tangents between two circles.Instructions:Draw two circles that share exactly three common tangents.Explanation:In geometry, a

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4. Draw two circles with 3 common tangents.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter9: Quadratic Functions And Equations

Section9.7: Solving Systems Of Linear And Quadratic Equations

Problem 21PPS

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Concept explainers

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.

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Question

**Exercise 4: Drawing Two Circles with Three Common Tangents**

Objective:
To understand and illustrate the concept of common tangents between two circles.

Instructions:
Draw two circles that share exactly three common tangents.

Explanation:
In geometry, a tangent to a circle is a straight line that touches the circle at exactly one point. Two circles can have up to four common tangents in various configurations. Your task is to draw two circles that have exactly three common tangents.

To achieve this:
1. **Draw two circles where one is inside the other but does not touch the other.** In this scenario, they share exactly one internal tangent and two external tangents.

Here is a step-by-step guide to construct such a figure:
1. **Draw the larger circle:**
- Use a compass to draw a large circle on your paper. Label the center of this circle as $ O_1 $.

2. **Draw the smaller circle inside the larger circle:**
- Place the compass at a suitable distance within the boundary of the larger circle and draw a smaller circle. Label the center of this smaller circle as $ O_2 $.

3. **Identify the three common tangents:**
- Draw the internal tangent: This is the line that touches both circles but stays inside the larger circle.
- Draw the two external tangents: These are the lines that touch both circles from the outside.

Visual aid:
- Ensure the circles do not intersect.
- Clearly indicate the tangents.

By completing this exercise, you will be able to visualize the geometric relationship between circles and their tangents, and fully understand the concept of common tangents.

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