a. The circle theorem that proves that angle ABC = angle AFC is angles subtended by the same arc are equal
b. The circle theorem that proves that angle ABC = angle EAC is angles subtended by the same arc are equal
How does the theorem work
When two angles subtend equal arcs in a circle, these angles are congruent.
This is a specific case of the angles subtended by the same arc are equal theorem, which states that if two angles subtend the same arc in a circle, then those angles are equal.
Applying this theorem to the figure, the subtended arc is AC. We can see that the angles that subtends this arc are:
EAC
AFC
ABC
Applying the theorem we say that the angles are equal
complete question
The diagram shows a circle with centre O and a tangent, DE, to the circle at A
a) Which circle theorem proves that angle ABC = angle AFC?
b) Hence, angle ABC = angle EAC. Which circle theorem does this prove?