Circle with triangles question

Question

O is the centre of the circle with points C, D and E on the circumference. The lines CE and OD intersect at F and CO is parallel to DE. Given that angle COD is 50 degree. Calculate angle ODC and Angle CED and angle CFD

Answer 1

OC=OD=OE (radii); triangles COD and DOE are isosceles; ODC=OCD=(180-50)/2=65;

angles COD and ODE are equal (alternate angles between parallel lines CO and DE); OED and ODE=50 (isosceles triangle DOE); angle EOD=180-50-50=80; COE=COD+EOD=50+80=130; OCE=OEC=(180-COE)/2=(180-130)/2=25; CED=OED-OEC=50-25=25; 

CFD=COD+OCE=50+25=75 (external angle of triangle OCF).

Required angles: ODC=65; CED=25; CFD=75 degrees.