If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD.

Question: If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD.

Solution:
Given that arcs AXB and CYD of a circle are congruent,
i.e. arc AXB ≅ arc CYD.

We know that if two arcs of a circle are congruent, their corresponding chords are also equal.
i.e. chord AB = chord CD

Thus, AB/CD = 1

AB/CD = 1/1
∴ AB : CD = 1 : 1