Tangent Circles and an Isosceles Triangle
The applet presents an 1803 Sangaku problem: Given a circle S with center O and diameter AC and point B on AC. Form circle G with center P and diameter AB and an isosceles triangle BCE with E on the circle S. Circle W with center Q is inscribed in the curvilinear triangle formed by circles S and G and the line BE. Prove that QB is perpendicular to AC.
(Years ago there was indeed a Java applet, now commented out since browers stopped supporting Java. Still, there are links to two pages with solutions to the problem.)
What if applet does not run? >One solution to this problem uses inversion and another makes use of inversion with negative power.
Sangaku

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