Circle Geometry (1 Viewer)

[cutemouse]

Could someone please help me with both parts?

Thanks

 

[Timothy.Siu]

i) angle ADE=angle ABC+angle BAF

angle ABC=angle ACB (iso. triangle)
angle BAF=angle BCF (angle on the same arc)

angle ADE=angle ACB+angle BCF
=angle ACF

ii)angle ACF=angle AGF (angle on the same arc)
angle ACF=angle ADE (part i)
so angle AGF=angle ADE
therefore DEGF is cyclic quad. (exterior angles of cyclic quad)