Garis singgung persekutuan luar dan garis singgung persekutuan dalam dua lingkaran

Introduction

This tutorial guides you through understanding and constructing external and internal tangents of two circles. These concepts are essential in geometry and have practical applications in various fields like engineering and design. By the end of this guide, you will be equipped to find and draw these tangents confidently.

Step 1: Understanding the Concepts of Tangents

Before diving into the construction, it’s important to grasp what tangents are:

• External Tangents: Lines that touch two circles at distinct points without intersecting the area between them.
• Internal Tangents: Lines that touch two circles at distinct points while intersecting the area between them.

Familiarize yourself with the properties of circles and tangents to enhance your understanding.

Step 2: Identifying the Circles

To begin, identify the two circles for which you want to find the tangents:

1. Let the first circle be centered at point A with radius r1.
2. Let the second circle be centered at point B with radius r2.
3. Measure the distance between the centers A and B (denote it as d).

Step 3: Checking Conditions for Tangents

Before constructing tangents, check the following conditions:

• For external tangents, ensure the distance d is greater than the sum of the radii (d > r1 + r2).
• For internal tangents, ensure the distance d is greater than the absolute difference of the radii (d > |r1 - r2|).

If these conditions are met, proceed with the construction.

Step 4: Constructing External Tangents

To draw the external tangents:

1. Draw both circles on a plane.
2. Connect centers A and B with a straight line.
3. Locate the midpoint M of line AB.
4. Draw a perpendicular bisector to line AB at midpoint M.
5. From point M, measure the distance equal to the difference in radii (|r1 - r2|) along the perpendicular bisector.
6. Mark points C and D on the perpendicular bisector.
7. Draw lines from points C and D to the points of tangency on each circle.

Step 5: Constructing Internal Tangents

To draw the internal tangents:

1. Using the same setup as before, keep circles A and B drawn and the line connecting centers A and B.
2. Again, find the midpoint M of line AB.
3. This time, measure the distance equal to the sum of the radii (r1 + r2) along the perpendicular bisector.
4. Mark points E and F at these distances.
5. Draw lines from points E and F to the points of tangency on each circle.

Conclusion

In this tutorial, you learned how to find and construct both external and internal tangents for two circles. Remember to always check the distance between the centers against the radii to confirm the existence of tangents. Practice these steps with different circle sizes to gain proficiency. Next, you may explore more advanced concepts in geometry, such as tangents to multiple circles or tangential polygons.