Analyze relationships among inscribed angles, central angles, circumscribed angles, radii, chords, diameters, and tangents.
Derive a named chord, arc, or central-angle relation
Problem
Starting from congruent chords \(AB\) and \(CD\) in the same circle, state the corresponding minor-arc relation and central-angle relation. Preserve endpoint pairing \(AB\) with \(CD\) and name the congruent-chords theorem that justifies \(\text{both}~\text{conclusions}\).
Congruent-circle-parts reasoning is a correspondence chain, so each chord must keep the same two endpoints as we move to arcs and central angles. We’ll confirm both chords lie in one circle, then use the congruent-chords theorem in the two requested directions.
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