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.

Tangent Circles and an Isosceles Triangle

(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

    [an error occurred while processing this directive]

|Activities| |Contact| |Front page| |Contents| |Geometry|

Copyright © 1996-2018 Alexander Bogomolny

[an error occurred while processing this directive]
[an error occurred while processing this directive]