Which is a true statement about any two congruent chords in a circle?A.They are equidistant from the center of the circle.B.They are perpendicular.C.They form an angle.D.They are parallel.SUBMITarrow_backPREVIOUS
Question
Which is a true statement about any two congruent chords in a circle?A.They are equidistant from the center of the circle.B.They are perpendicular.C.They form an angle.D.They are parallel.SUBMITarrow_backPREVIOUS
Solution
The true statement about any two congruent chords in a circle is A. They are equidistant from the center of the circle.
Here's why:
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A chord of a circle is a line segment whose endpoints lie on the circle.
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Congruent chords are chords that have the same length.
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The perpendicular from the center of the circle to a chord bisects the chord. This means it divides the chord into two equal parts.
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If two chords are congruent, then their distances from the center of the circle are equal. This is because the line drawn from the center of the circle to the chord (the perpendicular mentioned in step 3) is a radius of the circle, and all radii of a circle are equal in length.
Therefore, any two congruent chords in a circle are equidistant from the center of the circle.
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