Mathematics

The key insight is that equal chords in a circle subtend equal arcs from the center, which then determine equal inscribed angles. Since AB and AC are equal chords, they subtend equal arcs, meaning the arc lengths (or central angles) are the same. By the inscribed angle theorem, angles inscribed in equal arcs are equal—so the angles at B and C that "see" these equal arcs must be congruent.

The key insight is that equal chords in a circle subtend equal arcs from the center, which then determine equal inscribed angles. Since AB and AC are equal chords, they subtend equal arcs, meaning the arc lengths (or central angles) are the same. By the inscribed angle theorem, angles inscribed in equal arcs are equal—so the angles at B and C that "see" these equal arcs must be congruent.