Go Geometry Problems

Dynamic Geometry Problem 901: Intersecting Circles, Common External Tangent, Secant, Circumcircle, Concyclic Points, Cyclic Quadrilateral. GeoGebra, HTML5 Animation for Tablets (iPad, Nexus). Levels: School, College, Mathematics Education


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.

Dynamic Geometry Environment (DGE) or Interactive Geometry Software (IGS) of Problem 901

The interactive demonstration above was created with GeoGebra.

To stop/play the animation: tap the icon in the lower left corner.
To reset the interactive figure to its initial state: tap the icon in the upper right corner.
To manipulate the interactive figure: tap and drag points or lines.

GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus application, intended for teachers and students. Many parts of GeoGebra have been ported to HTML5. It has received several educational software awards in Europe and the USA.
See the static diagram of problem 901

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