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Geometry Problem 1118: Right Triangle, Angle Trisection, Concyclic Points, Cyclic Quadrilateral. Level: High School, SAT Prep, Honors Geometry, College, Math Education

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The figure below shows a right triangle ABC with AA1 and AA2 trisectors of angle BAC, similarly CC1 and CC2 trisectors of angle ACB. AA1 meets CC2 and CC1 at C3 and B1, respectively. AA2 meets CC2 and CC1 at B2 and A3, respectively. B1B2 meets AC at B3, B3C3 meets AA2 at A4, and B3A3 meets CC2 at C4. Prove that A3, B3, A4, B1 are concylic points, similarly B3, C3, Bv, C4 are concyclic points.
 

Infographic Geometry Problem 1118: Right Triangle, Angle Trisection, Concyclic Points, Cyclic Quadrilateral
 

 

 

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Last updated: May 4, 2015 by Antonio Gutierrez.