Arbelos and Inscribed Circle: Concyclic Points. Level: High School, SAT Prep, College

Online Geometry

Geometry Problem 638. If a circle is inscribed in the arbelos ACB with tangency points D, E, and F, as shown in the figure, then the points B, C, D, and F are concyclic on circle with center G and G is the midpoint of the semicircle of diameter BC. Similarly, A, C, E, and F are concyclic on circle with center H and H is the midpoint of semicircle of diameter AC.

 

 
 

 

See Also:

Arbelos, Theorems and Problems Index

Semicircle, Perpendicular, Inscribed Circle, Tangent, Chord

Geometry Problem 637
Semicircle, Diameter, Perpendicular, Inscribed Circle, Chord, Tangent, Arbelos.

Semicircle, Perpendicular, Inscribed Circle, Tangent

Geometry Problem 636
Semicircle, Diameter, Perpendicular, Inscribed Circle, Common Tangent.

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