Online Geometry theorems, problems, solutions, and related topics.
Geometry ProblemClick the figure below to see the complete problem 607.
Isosceles triangles ACF, BCE are similar.CF/CE = AC/BCCF.CB = CE.CA, and so A,B,F,E are concyclic.GBA, GFE are secants from G to the circle BAEF.GB.GA = GF.GE,x(x+10)= (8).(12), (x + 5)² = 121,x+5=11, x=6
< BEC = < BCE = < AFC Hence BAEF is cyclicSo 8 x 12 = x(x+10)Solving the quadratic for positive xx = 6Sumith PeirisMoratuwaSri Lanka