Japanese Theorem for Three Tangent Circles and a Triangle

​
distance from O to E
-0.7
-0.65
-0.5
-0.4
-0.3
-0.2
configuration
line AC
auxiliary lines and points
This Japanese classical theorem (Sangaku) deals with a configuration of three tangent circles (blue, purple and green) and an isosceles triangle that is tangent to one of the three circles (green) and has two of its vertices on the circumference of the largest circle (blue). The theorem states that the line joining the left vertex of the triangle to the center of the green circle is perpendicular to the horizontal diameter.

Details

Each of the three circles is tangent to the other two. The green circle is tangent to the side
AB
of the yellow isosceles triangle. The theorem states that the line from
A
to
C
is perpendicular to the diameter
GF
of the blue circle. You can change the position of the center of the purple circle.
Click the "configuration" button to see the triangle and circles. Click the "line AC" button to see the subject of the theorem. Click the "auxiliary points and lines" button to see the construction used in the proof of the theorem.

External Links

Sangaku Problem (Wolfram MathWorld)

Permanent Citation

Tomas Garza
​
​"Japanese Theorem for Three Tangent Circles and a Triangle"​
​http://demonstrations.wolfram.com/JapaneseTheoremForThreeTangentCirclesAndATriangle/​
​Wolfram Demonstrations Project​
​Published: August 4, 2022