## Monday, 5 October 2015

### P11: Verify the theorem: If two circles are touching circles then the common point lies on the line joining their centers.

Practical Name: Verify the theorem: If two circles are touching circles then the common point lies on the line joining their centers.
Tools/Software: Computer with Geogebra Software installed
Procedure:
 1. Start the Geogebra Software. Click on Tool No 5 and select ‘Circle with center through point’. 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’. 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 4. Click on Tool No 2 and select ‘Segment between two points’. 5. Click on ‘A’ followed by ’C’. 6. Click on Tool 1 and select ‘Point on Object’. 7. Click anywhere on Segment AC. A New Point ‘E’ will appear where you have clicked. 8. Drag the point ‘E’ till it lies on the point where the two circles touch each other. 9. Click on Tool 7 and select ‘Distance or Length’ Tool. 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’. 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.
Result:  The Theorem is verified.