Sangaku - Triangle and 3 Circles
Sangaku - Triangle and 3 Circles
From a 1803 Sangaku found in Gumma Prefecture.
The base of an isosceles triangle sits on a diameter of the large circle.
This diameter also bisects the circle on the left, which is inscribed so that it just touches
the inside of the container circle and one vertex of the triangle.
The top circle is inscribed so that it touches the outsides of both the left circle and the triangle,
as well as the inside of the container circle. A line segment connects the center of the top circle
and the intersection point between the left circle and the triangle.
Show that this line segment is perpendicular to the drawn diameter of the container circle.
(T. Rothman)
http://www.hermay.org/jconstant/wasan/sangaku/index.html
http://www.princeton.edu/main/news/archive/S15/04/04O77/