Class 10 Maths Chapter 11 Notes

Important full class 10 maths chapter 11 notes of Chords and Arcs of Mathematics 10th class by Dear Respectable Sir M. Ramzan Suib. These handwritten and Composed notes are very helpful in the preparation of class 10 maths chapter 11 notes for students of the 10th class Mathematics and these are according to the paper patterns of all Punjab boards.

• Important MCQs of Chapter No.11: Chords and Arcs of Mathematics 10th class.
• Important definitions of Chapter No.11: Chords and Arcs of Mathematics 10th class.
• Solutions of Chapter No.11: Chords and Arcs of Mathematics 10th class.
• Important problems of Chapter No.11: Chords and Arcs of Mathematics 10th class.
• Multiple Choice Questions. Four possible answers are given for the following questions. Tick the correct answer.
• (i) A 4 cm long chord subtands a central angle of 60°. The radial segment of this circle is:  (a) 1  (b) 2  (c) 3  (d) 4
• (ii) The length of a chord and the radial segment of a circle are congruent, the central angle made by the chord will be:  (a) 30°  (b) 45°  (c) 60°  (d) 75°
• (iii) Out of two congruent arcs of a circle, if one arc makes a central angle of 30° then the other arc will subtend the central angle of:  (a) 15°  (b) 30°  (c) 45°  (d) 60°
• (iv) An arc subtends a central angle of 40° then the corresponding chord will subtend a central angle of:  (a) 20°  (b) 40°  (c) 60°  (d) 80°
• (v) A pair of chords of a circle subtending two congruent central angles is:  (a) congruent  (b) incongruent  (c) over lapping  (d) parallel
• (vi) If an are of a circle subtends a central angle of 60°, then the corresponding chord of the arc will make the central angle of:  (a) 20°  (b) 40°  (c) 60°  (d) 80°
• If two arcs of a circle (or of congruent circles) are congruent, then the corresponding chords are equal.
• If two chords of a circle (or of congruent circles) are equal, then their corresponding arcs (minor, major or semi-circular) are congruent. In equal circles or in the same circle if two chords are equal they cut off equal arcs.
• Equal chords of a circle (or of congruent circles) subtend equal angles at the centre (at the corresponding centres).
• If the angles subtended by two chords of a circle (or congruent circles) at the centre (corresponding centres) are equal, the chords are equal.
• 1. In a circle two equal diameters AB and CD intersect each other. prove that m AD = m BC.
• 2. In a circle prove that the arcs between two parallel and equal chords are equal.
• 3. Give a geometric proof that a pair of bisecting chords are the diameters of a circle.
• Important definitions of Chapter No.10: Tangent to a circle:
• The boundary traced by a moving point in a circle is called its circumference whereas any portion of the circumference will be known as an arc of the circle.
• The straight line joining any two points of the circumference is called a chord of the circle.
• The portion of a circle bounded by an arc and a chord is known as the segment of a circle.
• The circular region bounded by an arc of a circle and its two corresponding radial segments is called a sector of the circle.
• A straight line, drawn from the centre of a circle bisecting a chord is perpendicular to the chord and conversely perpendicular drawn from the centre of a circle on a chord, bisects it.
• If two arcs of a circle (or of congruent circles) are congruent, then the corresponding chords are equal.
• If two chords of a circle (or of congruent circles) are equal, then their corresponding arcs (minor, major or semi-circular) are congruent.
• Equal chords of a circle (or of congruent circles) subtend equal angles at the centre (at the corresponding centres).
• If the angles subtended by two chords of a circle (or congruent circles) at the centre (corresponding centres) are equal, the chords are equal.
The boundary traced by a moving point in a circle is called its circumference whereas any portion of the circumference will be known as an arc of the circle.