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| Geogebra Practical 11 a Verify the theorem: If two circles are touching circles then the common point lies on the line joining their centers.Circles could either touch Internally or Externally. Case 1. Circles touching Externally. |
1. Open Geogebra. Click on Tool No 5 and select ‘Circle with center through point’. See Figure 1. |  Figure 1 |
2. Click at any place in the Graphic Area where you want one center ‘A’ of the first circle. Drag your mouse away from the center until you see a circle of appropriate size. Click to get point ‘B’. See Figure 2. |  Figure 2 |
3. Click on any point ‘C’ in the graphic area outside the first circle where you want the center of the second circle.Drag outward until the two circles are just touching. Click to get point ‘D’. See Figure 3. |  Figure 3 |
4. Click on Tool No 2 and select ‘Segment between two points’. See Figure 4. |  Figure 4 |
5. Click on ‘A’ followed by ’C’. See Figure 5. |  Figure 5 |
6. Click on Tool 1 and select ‘Point on Object’. See Figure 6. |  Figure 6 |
7. Click anywhere on Segment AC. A New Point ‘E’ will appear where you have clicked. See Figure 7. 8. Drag the point ‘E’ till it lies on the point where the two circles touch each other. |  Figure 7 |
9. Click on Tool 7 and select ‘Distance or Length’ Tool. See Figure 8 |  Figure 8 |
10. Click on Point ‘A’ followed by point ‘E’. Click on Point ‘E’ followed by point ‘C’. Click on Point ‘A’ followed by point ‘C’. See Figure 9. 11. In the Algebra Section verify that length(AC) = length(AE) + length(EC). This proves that A-E-C, i.e., the point of contact of two touching circles lies on the line joining their centers. |  Figure 9 |
George Ferrao
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