![]() In the above illustration, the length of chord PQ = 2√ (r 2 – d 2) Where r = the radius of a circle and d = the perpendicular distance from the center of a circle to the chord. If the length of the radius and distance between the center and chord is known, then the formula to find the length of the chord is given by, The length of a chord, given the radius and distance to the center of a circle.Each formula is used depending on the information provided. There are two formulas to find the length of a chord. For example, chord AB is equal to chord CD if PQ = QR. Two chords are equal in length if they are equidistant from the center of a circle.Two radii joining the ends of a chord to the center of a circle form an isosceles triangle.The diameter is the longest chord of a circle, whereby the perpendicular distance from the center of the circle to the chord is zero.The length of a chord increases as the perpendicular distance from the center of the circle to the chord decreases and vice versa. ![]() The radius of a circle is the perpendicular bisector of a chord.In the circle below, AB, CD, and EF are the chords of the circle. The diameter of a circle is considered to be the longest chord because it joins to points on the circumference of a circle. ![]()
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