Online Geometry theorems, problems, solutions, and related topics.
Geometry ProblemLevel: Mathematics Education, High School, Honors Geometry, College.Click the figure below to see the complete problem 687.
Let A’, B’, C‘ are contacting points of encircles to BC, AC and AB Per 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 = 1So AA3, BB3 and CC3 are concurrent per Ceva’s TheoremPeter Tran
Typos: rhs's ofA’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