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Theorems About Chords

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The line segment drawn perpendicular to a chord from the center of the circle bisects the chord.

PROOF

From the chords taken in a circle or in congruent circles, the one that is nearer to the center is longer.
In a circle or in congruent circles, congruent chords are equidistant from the center. Geometric place of the midpoints of these chords is a circle.
From the chords that pass through a point taken inside a circle, the one that is perpendicular to the radius at that point is the smallest.
Chords of the same length in the same circle cut congruent arcs.
Parallel chords in the same circle always cut congruent arcs. The quadrilateral formed is an isosceles trapezoid.

You can change the angles by moving the points.

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