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We study some properties of a triad of circles associated with a triangle. Each circle is inside the triangle, tangent to two sides of the triangle, and externally tangent to the circle on the third side as diameter. In particular, we find a nice relation involving the radii of the inner and outer Apollonius circles of the three circles in the tria...
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... The sangaku gave a relationship involving the radii of the three circles. Additional properties of this configuration were given in [29] and [30]. For example, in Figure 2 (left), the three blue common tangents are all congruent. ...
... We can generalize many of the results in [30] by replacing the semicircles with arcs having the same angular measure. Let ω a , ω b , and ω c be arcs with the same angular measure θ erected internally on the sides of ABC as shown in Figure 48. ...
... When θ = 180 • , the arcs become semicircles, t = 1, and this result agrees with Theorem 6.1 in [30]. ...
We study properties of certain circles associated with a triangle. Each circle is inside the triangle, tangent to two sides of the triangle, and externally tangent to the arc of a circle erected internally on the third side.