Question

Two circles with different radii have chords A B ¯ and C D ¯, such that A B ¯ is congruent to C D ¯. Are the arcs intersected by these chords also congruent? Explain.

• 5 points for the correct answer
• 5 points for a thoughtful and correct explanation

Hint:

It would be helpful to draw two circles and label them according to the given information, then evaluate possible arc measures.
Consider the type of triangle that may be drawn by connecting the endpoints of a chord to the center of a circle. Compare the triangles made by two circles with different radii.

Answer 1

• 2 circles 'p' with radius10 mm and 'q' with radius 6mm.
• The chord AB and CD are of same length, But we can see the triangle OAB and OCD formed when joining the end point of chord with the center O is not congruent.
• Then the arcs AB and CD never be congruent.
• There is only one chance to get congruent arc with same chord length , that is from a pair of congruent circle (with same radii)
• We can see clearly in this enlarged view below. 2 arcs are not congruent.
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