Online Geometry theorems, problems, solutions, and related topics.
Geometry Problem. Post your solution in the comments box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the figure below to view more details of problem 1177.
We can write 4 simple equations y+e = c.......(1)x+d = a........(2)c/b = x/d.......(3)a/b = y/e.......(4)Now we can eliminate a,b,c between these 4 equations.From (3') & (4) dc/x = ae/y and so from (1) and (2)d(y+e)/x = e(x+d)/ySimplifying x^2e + xde + y^2d + ydeSumith PeirisMoratuwaSri Lanka
Manoloudis Apostolis 4 Lyceum of Korydallos-GreeceEven AB=c BC=a AC=b.Then x.e.(x+d)=y.d.(y+e) x.e,a=y.d.c By theorem bisectors c/b=x/d and x=a.c/(b+c) d=a.b/(b+c) and a/b=y/e y=a.c/(a+b) e=b.c/(a+b).x.e.a=a.c/(b+c).b.c/(a+b).a=y.d.c .
apply two times bisector´s theorem First for AD, and second for CE