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
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
Home
|
Search | Geometry
|
Problems |
All Problems |
Open Problems
|
Visual Index
|
10 Problems
|
Problems Art Gallery
|
Art |
901-910
|
Dynamic
Geometry
|
GeoGebra |
Circle
|
Intersecting Circles
|
Tangent Line
|
Circumcircle
|
Concyclic
Points
|
Cyclic Quadrilateral
|
iPad Apps
|
Nexus 7 Apps
| Projects
|
Email
|
Solution/Comment | by Antonio Gutierrez
|