If the line segment DE is a diameter of a circle with centre C, and F is any other point on
the circle, prove that (in Euclidean geometry) angle DFE is a right angle.
Suppose that G is yet another point on the circle, such that FG passes through C. Prove
that FE is parallel to DG.

Question

anonymous · Answer

OG=OE and OF =OD  and  angles O1 = O2
two triangles have congruity. ( DOG and FOE). 
so DG=FE
we can proof same congruity for tiangles DOF and GOE.
so DF=GE

anonymous · Answer

so DGEF is parallelogram.