Are the chords congruent?

Question

Chords: AB and BC create the segment AC in a circle. If AB has a 90 degree angle and BC does not, are the chords congruent?

Answer 1

No, the segment AB measures √(R²+ R²) = R√2

The other segment will be equal to AB = √(R² + R² - 2R²cosθ). The only way that they are congruent is when θ = 90 otherwise they are different.