POINT • CIRCLE • CIRCLE
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Two Tangent Circles Of Different Sizes, Point Lies On The Common Tangent Line Which Passes Through The Tangent Point Of The Circles
Number of solutions: 2
GeoGebra construction
Steps
- This task will be solved using a set of points which can be used to draw a hyperbola. Lets two draw lines through point C and the points A and B respectively. Name the intersections of these lines.
- Find the centerpoint between these intersections and the point C. These points are on the desired hyperbola.
- Using one center of a circle and the point C as focus points and a point from step two which lies on the hyperbola construct a hyperbola. Repeat this for all four of the points constructed in step two - four hyperbolas should be constructed.
- The intersections of these hyperbolas are the centers of the wanted circles. Call these points S1 and S2.
- Draw the final circles with their center in points S1 and S2 respectively and passing through point C.
- Continue using the process of solving the circle, circle, point solutions.