perplexus.info :: Geometry : Congruent Incircles II

Congruent Incircles II (Posted on 2008-05-11)

Let D be a point on side BC of triangle ABC.

If the incircles of triangles ABD and ACD are congruent, then what is the length of the cevian AD in terms of a, b, and c ?

See The Solution Submitted by Bractals

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

Puzzle Thoughts

Comment 6 of 6 |

AD = SQRT((a - SQRT(b2 - 4/a2 * ((a+b+c)/2 * ((a+b+c)/2 - a)* ((a+b+c)/2 - b) * ((a+b+c)/2 - c)) + 4/a2 * ((a+b+c)/2 * ((a+b+c)/2 - a) * ((a+b+c)/2 - b) * ((a+b+c)/2 - c))

Posted by K Sengupta on 2023-04-16 23:10:01

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info