Static Geometry Problem 901: Intersecting Circles, Common External Tangent, Secant, Circumcircle, Concyclic Points, Cyclic Quadrilateral. Mathematics Education. Distance learning.

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Static Diagram Geometry Problem 901: Intersecting Circles, Common External Tangent, Secant, Circumcircle, Concyclic Points, Cyclic Quadrilateral. Levels: School, College, Mathematics Education

Dynamic Geometry Problem 901: Intersecting Circles, Common External Tangent, Secant, Circumcircle, Concyclic Points, Cyclic Quadrilateral.

The circles O and O₁ intersect at A and B (see the figure above), CD is the common external tangent, CA intersects circle O₁ at E, DA intersects circle O at F, FC and ED intersect at G, BA intersects FG at H. If the circumcircle of triangle EFG intersects circle O₁ at J, prove that the points B, C, H, J are concyclic.
See the dynamic diagram of problem 901