Explain how you know ABbar TildeFullEqual CDbar given E is t

Explain how you know AB^bar TildeFullEqual CD^bar, given E is the center of the circle. (Include Theorem numbers.)

Solution

From the figure EF is perpendicular to AB and EG is perpendicular to DC. Also it is given that EF = EG

Then by the theorem of chords which states that if the perpendicular distance from the center to 2 chords are the same, then the 2 chords are equal. Therefore Chord AB is equal to chord DC.