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Assume that two chords in a given circle are the same distance from the center of the circle Which of the following must also be true?
They must be congruent.
Two chords that are the same distance from the center of a circle must be?
congruent
What must be true before using corresponding parts of congruent triangles are congruent in a proof?
The triangles must be congruent.
Does a diameter that is perpendicular to a chord bisect the chord?
Yes, any diameter which is perpendicular to a chord bisects said chord. This can be proved most easily with a picture, but is proved using a congruent triangle proof. Both triangles include the points at the center of the circle and the intersection of the diameter and chord. The other points should be the endpoints of the chord. They are congruent by hypotenuse leg; it was given that they are right triangle by the "perpendicular", the "leg" is the segment between the center of the circle and the intersection, and it is equal in both triangles because it is the same segment in both triangles. The hypotenuses are equal because both are radii of the circle. Because the triangles are congruent, their sides must be so the two halves of the chord are congruent, and therefore the chord is bisected by the diameter.
Are points of a circle coplanar?
Yes. A circle is defined as the set of all points in a plane equidistant from a given point (the center of the circle) - hence - all points of a circle must be co-planar by definition.
