CIRCLE • CIRCLE • CIRCLE
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Download GeoGebra file
Download GeoGebra file
Three Externally Tangent Circles With Same Size
Number of solutions: 3
GeoGebra construction
Steps
- Draw three lines i, g and h, each passing through the centre of one of the circles and the point of contact of the other two circles.
- Denote the intersection of these three lines as S1, and this point is the centre of the two circles sought.
- Their radii are determined by the lengths of the segments S1G and S1F, where G and F are the intersections of the line i and the circle b(works with any circle and its intersecting line).
GeoGebra construction
Steps
Procedure
- Dilate the circles into points.
- Connect the points with line segments.
- Find the center of the resulting triangle using angle bisectors.
- Construct the circumcircle of this triangle – this circle passes through all the points.
- Dilate this circle by the radius of the original circles, both towards and away from the center.
GeoGebra construction
Steps
Procedure
- Create a circle tangent to the third circle at one of the common points of the two given circles.
- Invert all given circles with respect to the newly created circle.
- Proceed as in the problem "Parallel lines, both tangent to a circle."
- Invert both solution circles with respect to the circle created in step one.