Do you find it too trivial to find the center and radius of the incircle or the circumcircle? Then try and find the center and radius of the Kenmotu circle! Indeed, each triangle has exactly one Kenmotu circle: its intersections with the edges are the contact points of three equal squares, each of which has two vertices on the triangle and which share a common vertex. This common vertex, the Kenmotu point, is the center of the circle.
Sangaku problems are geometric problems of the type found on devotional mathematical wooden tablets ("sangaku"), which were hung under the roofs of shrines or temples in Japan. Shoto Kenmotu (1790–1871) was one of the Japanese mathematicians who developed their own "traditional mathematics".