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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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Context 1
... 6.1. In Figure 15 showing the triad of circles associated with ABC and the inner Apollonius circle externally tangent to each circle in the triad, we have that the sum of the yellow areas is equal to the green area. Let ρ o be the radius of the outer Apollonius circle internally tangent to γ a , γ b , γ c (see Figure 16). ...
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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.
