These are some of the basic theorems on the chords and arcs of a circle. This means that they all lie on the same circle. Theorem 10: If the line segment joining any two points subtends equal angles at two other points that are on the same side, they are concyclic. Theorem 9: Angles formed in the same segment of a circle are always equal in measure.ġ0. Theorem 8: The angle subtended by an arc at the center of a circle is double that of the angle that the arc subtends at any other given point on the circle.ĩ. It states that chords equidistant from the center of a circle are equal in length.Ĩ. Theorem 7: This is the converse of the previous theorem. Theorem 6: Equal chords of a circle are equidistant from the center of a circle.ħ. Theorem 5: If there are three non-collinear points, then there is just one circle that can pass through them.Ħ.

In other words, any line from the center that bisects a chord is perpendicular to the chord.ĥ. Theorem 4: The line that is drawn through the center of the circle to the midpoint of the chords is perpendicular to it. It means that both the halves of the chords are equal in length.Ĥ. Theorem 3: A perpendicular dropped from the center of the circle to a chord bisects it. Cyclic Quadrilateral and Intersecting / Non-intersecting Circlesģ.It implies that if two chords subtend equal angles at the center, they are equal. Theorem 2: This is the converse of the previous theorem. Theorem 1: Equal chords of a circle subtend equal angles at the center.Ģ.Let us now look at the theorems related to chords of a circle. You already know about the concepts of arc and circumference. T A Segment of the circle is the region that lies between the Chord and either of Arcs. Chord is derived from a Latin word “ Chorda” which means “ Bowstring“. It is the longest chord possible in a circle. Diameter is the Chord that passes through the center of the circle. The endpoints of this line segments lie on the circumference of the circle. A Chord is a line segment that joins any two points of the circle.

Circle geometry theorems