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Diagram Properties If two chords are equidistant from the centre of a circle, then the chords are congruent. If FO EO then CD AB If two chords in a circle are congruent, then they are equidistant from the centre of the circle. If CD AB then FO EO A line that is perpendicular to a chord and passes through the centre of a circle bisects the chord. A perpendicular bisector is a line that passes through the midpoint of a line segment and is perpendicular to that line segment. Perpendicular bisectors of any two or more chords of a circle pass through and intersect at the centre of that circle. A line segment joining the midpoint of a chord and the centre of the circle is perpendicular to the chord. The measure of the minor arc is equal to the measure of the central angle subtended by the arc. A central angle is the angle with endpoints on the arc of a circle and vertex at the centre. The measure of the inscribed angle subtended by an arc is equal to one-half the size of the arc. An inscribed angle is the angle with endpoints on the arc of a circle and vertex on the circumference of the circle. The measure of the inscribed angle subtended by the same arc as its central angle is equal in measure to one-half the measure of the central angle. An angle subtended by the diameter of a circle is always equal to 900. Two or more inscribed angles subtended by the same arc are equal in measure. If a quadrilateral is inscribed in a circle, it is called a cyclic quadrilateral. Opposite angles in a cyclic quadrilateral are supplementary (add to 1800). A cyclic quadrilateral has all four vertices on the circumference of the same circle.. A line drawn tangent to a circle meets the radius of the circle at a right angle. A tangent to a circle is perpendicular to the radius that meets it. The measure of an angle between a tangent and a chord of a circle is equal to the measure of the inscribed angle opposite it. A chord divides a circle into two arcs. The smaller arc is called the minor arc. The larger arc is called the major arc. The part of a circle that is formed by the arc and a chord is called a segment. Shape Proof Formulas to use Rectangle Prove opposite sides are equal. Prove adjacent sides are perpendicular. Distance formula Slope formula Square Prove opposite sides are equal. Prove adjacent sides are perpendicular. Distance formula Slope formula Parallelogram Prove opposite sides are equal. Prove opposite sides are parallel Distance formula Slope formula Rhombus Prove all sides are congruent. Prove opposite sides are parallel. Distance formula Slope formula Trapezoid Prove one pair of opposite sides are parallel. Slope formula Right Triangle Prove adjacent sides are perpendicular. Slope formula Isosceles Triangle Prove two sides are congruent. Distance formula Equilateral Triangle Prove three sides congruent. Distance formula Scalene Triangle Prove no sides congruent. Distance formula