Dynamic Geometry 1479: Triangle, Circumcircle, Angle Bisector, Perpendicular Bisector, Chord, Concyclic Points, Parallel Lines, Step-by-step Illustration
For a triangle ABC with circumcircle c1 and internal angle bisector BD (see diagram) let EF be perpendicular to BD, GH perpendicular bisector of AE, and JK perpendicular bisector of CF. Chord HL passes through E and chord KM passes through F, Prove that (1) Points M, E, F, and L are concyclic; (2) EF and HK are parallel.
Static Diagram of Problem 1479
Poster of problem 1479 using iPad Apps
Search gogeometry.com
Classroom Resource:
Interactive step-by-step animation using GeoGebra
This step-by-step interactive illustration was created with GeoGebra.
- To explore (show / hide): click/tap a check box.
- To stop/play the animation: click/tap the icon in the lower left corner.
- To go to first step: click/tap the "Go to step 1" button.
- To manipulate the interactive figure: click/tap and drag the blue points or figures.
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.
Recent Additions
Geometry Problems
Open Problems
Visual Index
Ten problems: 1411-1420
All Problems
Triangle
Circle
Triangle Centers
Circumcircle
Angle Bisector
Parallel lines
Perpendicular lines
Perpendicular
Bisector
Chord
Concyclic
Points
GeoGebra
HTML5 and Dynamic Geometry
iPad Apps
View or Post a solution