<p>Math 12 The Chord and its Properties . . . </p><p>Key Words:</p><p>Chord – </p><p>Statement (Property) One: Chords equidistant from the centre of a circle are congruent.</p><p>Converse: Congruent chords are equidistant from the centre of the circle.</p><p>If and Only If Statement (iff): Chords are congruent iff they are equidistant from the centre of the circle. A C Circle with centre O Chord AB is congruent to chord CD. O Chord AB and chord CD equidistant from centre. B D (Note – distances are measured perpendicular to chords!)</p><p>Statement (Property) Two: A line perpendicular to a chord that passes through the centre of the circle bisects the chord.</p><p>Converse: A line that is perpendicular to a chord and bisects the chord passes through centre.</p><p>If and Only If Statement: A line perpendicular to a chord bisects the chord iff it passes through centre.</p><p>A C Circle with centre O Perpendicular bisector of chord AB passes through centre. Perpendicular bisector of chord CD passes through centre. O</p><p>B D</p><p>Chord Worksheet: 1. Determine the indicated values. a) Length of AB. b) Length of r. c) Length of AB A B 15 O 2 9 O O r A 6 3 B</p><p>14 8 16</p><p>2. In the following circle the radius is 30 cm. The chord PQ is perpendicular to the diameter AOB. If O is circle center and PQ is 48 cm, find the length of AS. Q</p><p>A ▪O S B</p><p>P 3. In a circle, a chord is 16 cm in length and is 6 cm from the centre of a circle. Calculate the length of the diameter.</p><p>4. Two parallel chords of a circle, MN and PQ have lengths 12 cm and 16 cm. If the diameter of the circle is 20 cm, find the perpendicular distance between the chords. </p><p>5. A circle with center O has a diameter of 26 cm. A chord, PQ, is 24 cm in length. How far is the chord from the centre of the circle?</p><p>6. In a circle with centre O, a chord PQ is 16 cm in length. If T is a point of the chord such that OT  PQ and OT = 5 cm, calculate the length of the radius.</p><p>7. A diameter and a chord of a circle have a common end point. If the length of the diameter is 36 cm and the length of the chord is 16 cm, how far is the chord from the center of the circle?</p><p> n 2  m2 8. Refer to the figure given. Show that x  2x  2 4 m O n 2x  2</p>