7. How many common tangent lines can be drawn to the circles shown below? Draw them.

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
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**Question 7: How many common tangent lines can be drawn to the circles shown below? Draw them.**

Below is an image displaying two circles of different sizes. The left circle is larger and both circles have centers marked with a dot.

**Explanation of the Diagram:**

The diagram features two distinct circles. The circle on the left is larger, and the circle on the right is smaller. Both circles have their centers indicated by dots. The centers are visually aligned horizontally.

To solve the given problem, you need to determine the number of common tangent lines that can touch these two circles without intersecting the interior of either circle. You then need to draw these tangent lines.

**Additional Information:**

A tangent line to a circle is a straight line that touches the circle at exactly one point. When dealing with two circles, there are two types of common tangent lines:

1. **External Tangents:** Lines that touch both circles but don't intersect the region between them.
2. **Internal Tangents:** Lines that touch both circles but cross the segment joining the centers of the circles.

For two circles that do not intersect, there are generally four possible common tangents: two external and two internal.

This concept is valuable in understanding the geometric relationship between circles and how lines can interact with them uniquely.
Transcribed Image Text:**Question 7: How many common tangent lines can be drawn to the circles shown below? Draw them.** Below is an image displaying two circles of different sizes. The left circle is larger and both circles have centers marked with a dot. **Explanation of the Diagram:** The diagram features two distinct circles. The circle on the left is larger, and the circle on the right is smaller. Both circles have their centers indicated by dots. The centers are visually aligned horizontally. To solve the given problem, you need to determine the number of common tangent lines that can touch these two circles without intersecting the interior of either circle. You then need to draw these tangent lines. **Additional Information:** A tangent line to a circle is a straight line that touches the circle at exactly one point. When dealing with two circles, there are two types of common tangent lines: 1. **External Tangents:** Lines that touch both circles but don't intersect the region between them. 2. **Internal Tangents:** Lines that touch both circles but cross the segment joining the centers of the circles. For two circles that do not intersect, there are generally four possible common tangents: two external and two internal. This concept is valuable in understanding the geometric relationship between circles and how lines can interact with them uniquely.
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