Angles Of Intersecting Chords

Geometry Level 1

Two intersecting chords of a circle make equal angles with the diameter through their intersection.

Are the lengths of the chords equal?

Always Sometimes Never

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Vishwathiga Jayasankar by vishwathiga jayasankar , 20, India

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2 solutions

Chung Kevin
Mar 15, 2016

Since the angles are equal, we see that there is a reflection symmetry with respect to the diameter that goes through their intersection.

This tells us that the two intersecting chords will always be of equal length.

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Brendix Emata
Mar 16, 2016

Vertical angles are congruent. If one of them is congruent to its adjacent angle, then by transitivity, the fourth angle is congruent to its adjacent. And thus, two isosceles triangles are formed. The two chords must be of equal length.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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