Let ABC be a triangle with incenter I. Let AB and AC intersect the circle through B, I, and C at D and E, respectively, besides B and C. Then BD = CE.
THINGS TO TRY
See problem 2.91(b) in V. Prasolov,
Problems in Plane and Solid Geometry
, Vol. 1,
[PDF], (D. Leites, ed. and trans.).
the Wolfram Demonstrations Project
Embed Interactive Demonstration
More details »
Download Demonstration as CDF »
Download Author Code »
More by Author
Two Triangles of Equal Area on Either Side of an Angle Bisector
Intersection of an Altitude and a Line through the Incenter
A Concurrency from the Reflection of the Incircle's Contact Points across the Incenter
On the Areas of Triangles Associated with an Excircle
Relations between Some Triangles Associated with Excircles
Division of an Angle Bisector by the Incenter
The Line through the Incenter and Circumcenter
A Collinearity Involving an Excircle, the Incircle, and the Circumcircle
Collinearity of a Triangle's Circumcenter, Incenter, and the Contact Triangle's Orthocenter
The Schiffler Point
High School Geometry
High School Mathematics
Browse all topics
The #1 tool for creating Demonstrations
and anything technical.
Explore anything with the first
computational knowledge engine.
The web's most extensive
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
STEM Initiative »
Programs & resources for
educators, schools & students.
Join the initiative for modernizing
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
© 2018 Wolfram Demonstrations Project & Contributors |
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have