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Mathematics · Class 10 · Chapter 25: Chords of a Circle

8 min

Key points

A chord is a line segment that joins any two points on a circle
The diameter is the longest chord of a circle passing through the center
Equal chords of a circle are equidistant from the center
The perpendicular from the center of a circle to a chord bisects the chord
Equal chords subtend equal angles at the center of the circle
If two chords intersect inside a circle, the product of their segments are equal
The angle in a semicircle is always a right angle (90°)
Chords equidistant from the center of a circle are equal in length

Definitions

Chord: A chord is a straight line segment whose endpoints both lie on the circle
Diameter: A diameter is a chord that passes through the center of the circle and is the longest possible chord
Perpendicular Bisector: A perpendicular bisector of a chord is a line that passes through the center of the circle and is perpendicular to the chord, dividing it into two equal parts
Arc: An arc is a portion of the circumference of a circle between two points on the circle
Segment: A segment is the region of a circle bounded by a chord and the arc subtended by the chord

Worked example

Define chord of a circle. Prove that the perpendicular drawn from the center of a circle to a chord bisects the chord. (6 marks)

A chord is a straight line segment joining any two points on circumference. Proof shows perpendicular from center creates two congruent right triangles, making the foot of perpendicular the midpoint of chord.

Common mistakes

Students confuse chord with diameter - remember diameter is a special chord passing through center
Forgetting to state the theorem before applying it in proofs
Not drawing proper diagrams with clear labels for center O and chord points
Mixing up the intersecting chords theorem with other circle theorems
Not mentioning that perpendicular from center bisects the chord AND the arc

Quick recap

Chord is a straight line segment joining two points on circumference. Diameter is the longest chord passing through center. Perpendicular from center bisects any chord. Equal chords are equidistant from center.

Generated by AI from Sindh Textbook Board material; review state: ai_unreviewed. MCQs, past-paper references and examiner notes are held back until a teacher has checked them.