Geometry Problem
Level: Mathematics Education, High School, Honors Geometry, College.
Click the figure below to see the complete problem 687.
Wednesday, November 9, 2011
Problem 687: Triangle, Excircles, Tangency points, Tangent lines, Concurrent Lines
Subscribe to:
Post Comments (Atom)
Let A’, B’, C‘ are contacting points of encircles to BC, AC and AB
ReplyDeletePer the result of problem 682, 3, B3 and C3 are Gergonne points
AA3 will cut BC at A’ and A’B/A’C= (s-a)/(s-b)
Similarly B’C/B’A=(p-a)/p-c) and C’A/C’B=(s-b)/(s-a)
And A’B/A’C . B’C/B’A . C’A/C’B = 1
So AA3, BB3 and CC3 are concurrent per Ceva’s Theorem
Peter Tran
Typos:
ReplyDeleterhs's of
A’B/A’C= (s-a)/(s-b),
B’C/B’A=(p-a)/p-c)and
C’A/C’B=(s-b)/(s-a)
to be corrected as
(s-c)/(s-b),
(s-a)/(s-c)and
(s-b)/(s-a)respectively