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About Apollonian Problems
Problems of Apollonius' and Pappus'
Euclidean geometry (and history) and construction
Non-Euclidean solutions to the Problem of Apollonius
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Utilized Methods
Dilation
Circle Inversion
Loci Of Points Satisfying Certain Properties
Power of a point to a circle
Translation
Homothety
CIRCLE • LINE
Circle And Line With Contact
Number of solutions: ∞
SOLUTION METHOD
Loci Of Points Satisfying Certain Properties
GeoGebra construction
Download GeoGebra file
Steps
Draw the line p
1
passing through the points B and S
1
, the resulting line h is one of the solutions
Construct a circle centered at B and passing through S
1
Through the resulting point C, which is the intersection of the line h and the circle e, we draw a line parallel to p
1
and name it p
2
Construct a parabola over the line p
2
with a focus at point S
1