# Class 10 Math Chords and Arcs (vii) The semi circumference and the diameter of a circle both subtend a central angle of:(a) 90^{\circ} (b) 180^{\circ} (c) 270^{\circ} (d) 360^{\circ}

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##### (vii) The semi circumference and the diameter of a circle both subtend a central angle of:(a) 90^{\circ} (b) 180^{\circ} (c) 270^{\circ} (d) 360^{\circ}

Example 1: The internal bisector of a central angle in a circle bisects an arc on which it stands.

(v) A pair of chords of a circle subtending two congruent central angles is:(a) congruent(b) incongruent(c) over lapping(d) parallel

2 . In a circle prove that the arcs between two parallel and equal chords are equal.

(iii) Out of two congruent arcs of a circle if one arc makes a central angle of 30^{\circ} then the other arc will subtend the central angle of:(a) 15^{\circ} (b) 30^{\circ} (c) 45^{\circ} (d) 60^{\circ}

(x) The arcs opposite to incongruent central angles of a circle arc always:(a) congruent(b) incongruent(c) parallel(d) perpendicular

(viii) The chord length of a circle subtending a central angle of 180^{\circ} is always:(a) less than radial segment(b) equal to the radial segment(c) double of the radial segment(d) none of these

Example 1: A point P on the circumference is equidistant from the radii \overline{O A} and O B . Prove that m \overparen{A P}=m \overparen{B P}

(i) A 4 \mathrm{~cm} long chord subtands a central angle of 60^{\circ} . The radial segment of this circle is:(a) 1(b) 2(c) 3(d) 4

4. If C is the mid point of an arc A C B in a circle with centre O . Show that line segment O C bisects the chord A B .

1. In a circle two equal diameters \overrightarrow{A B} and \overrightarrow{C D} intersect each other. Prove that m \overline{A D}=m \overline{B C} .

(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^{\circ} (b) 45^{\circ} (c) 60^{\circ} (d) 75^{\circ}

(vi) If an arc of a circle subtends a central angle of 60^{\circ} then the corresponding chord of the arc will make the central angle of:(a) 20^{\circ} (b) 40^{\circ} (c) 60^{\circ} (d) 80^{\circ}

3 . Give a geometric proof that a pair of bisecting chords are the diameters of a circle.

Example 2: In a circle if any pair of diameters are I each other then the lines joining its ends in order. square.

(ix) If a chord of a circle subtends a central angle of 60^{\circ} then the length of the chord and the radial segment are:(a) congruent(b) incongruent(c) parallel(d) perpendicular