The Triangle Formed by the Centers of the Miquel Circles

A'

B'

C'

∠ABC

≈

61.36°

∠ACB

≈

75.02°

∠BAC

≈

43.62°

∠A''B''C''

≈

61.36°

∠A''C''B''

≈

75.02°

∠B''A''C''

≈

43.62°

Let ABC be a triangle. Let A', B', and C' be points on BC, AC, and AB, respectively. Let A'', B'', and C'' be the circumcenters of AB'C', BA'C', and CA'B', respectively. Then A"B''C'' is similar to ABC.