Mathematics
Mathematics
Problem
Fill in the blank: In a circle, equal chords subtend ______ angles at the centre.Intuitive explanation
When two chords have the same length, they "reach out" from the circle's edge the same distance. The key insight is that the central angle—the angle formed at the center by the two radii connecting to a chord's endpoints—is entirely determined by the chord's length. Longer chords create wider angles; equal chords must create equal angles. This relationship is one of the fundamental symmetries of circles.
Intuitive explanation
When two chords have the same length, they "reach out" from the circle's edge the same distance. The key insight is that the central angle—the angle formed at the center by the two radii connecting to a chord's endpoints—is entirely determined by the chord's length. Longer chords create wider angles; equal chords must create equal angles. This relationship is one of the fundamental symmetries of circles.