So OGD angle =90 degrees.
Angle OHC=90 degrees
OG, oh oh, respectively, ad AD, BC.
So AG=DG= 1/2AD.
BH=CH= 1/2BC
So triangle OGD and triangle OHC are right triangles.
Because OE divides AEC in two.
So angle OEA= angle OEC= 1/2 angle AEC.
Because OE=OE
So triangle OEG and triangle OEH are congruent (AAS)
So OG = oh
Because OD=OC
So the right triangle OGD congruent right triangle OHC (HL)
So DG=CH
So AD=BC
So arc ABD= arc CDB.
So arc AB= arc CD
So AB=CD
(2) Solution: Because AD is perpendicular to CB.
So the angle AEC=90 degrees
Because angle OEA= angle OEC= 1/2 angle AEC (authentication)
So the angle OEA=45 degrees
Because OGD angle =90 degrees (proved)
So the triangle OGD is a right triangle.
So od 2 = DG 2+og 2.
Because angle OGD+ angle OEA+ angle GOE= 180 degrees.
So the angle θ= 45 degrees
So angle GOE= angle OEA=45 degrees.
So EG=OG
Because the radius of circle O is 5
So OD=5
Because DG=DE+EG
DE= 1
So EG=3
DG=4
Because DG=AG= 1/2AD
So AD=8
So the length of AD is 8.