Main point:

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So, these solutions are applicable for all these boards also. All the questions are explained well using the theorems of circles and giving proper examples.

In few questions some axioms of circles are also used as theorems. Study Material for What do understand by a circle? What are the components of a circle? What are the main Properties related to a circle? Important Theorems on Circles Class 9 Maths Chapter 10 Equal chords of a circle are equidistant from the centre and cords equidistant from the centre of a circle are equal.

If two arcs of a circle are congruent, then their corresponding chords are equal and conversely if two chords of a circle are equal, then their corresponding arcs are congruent. Congruent arcs of a circle subtend equal angles at the centre. The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Angles in the same segment of a circle are equal. Angle in a semi-circle is a right angle. The sum of either pair of opposite angles of a cyclic quadrilateral is and if the sum of a pair of opposite angles of a quadrilateral is , then the quadrilateral is cyclic.

The centre of a circle lies in interior of the circle. A circle has only finite number of equal chords. True or False? Because, there are infinite number of equal chords in a circle.

Ex Fill in the blanks. Solution: i interior ii exterior iii diameter iv semicircle v the chord vi three. Write True or False. Give reason for your answers. Recall that two circles are congruent, if they have the same radii.

Prove that, if chords of congruent circles subtend equal angles at their centres, then the chords are equal. Draw different pairs of circles.

How many points does each pair have in common? What is the maximum number of common points? Solution: Let us draw different pairs of circles as shown below: We have. Suppose you are given a circle. Give a construction to find its centre.

Solution: Steps of construction : Step I : Take any three points on the given circle. Let these points be A, B and C. If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common Class 9 Maths Ch 10 Ex 10.2 Eng chord. Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm.

Find the length of the common chord. Let PQ be the common chord. If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.

Join OE. If two equal chords of a circle intersect within the circle, prove that Ch 10 Maths Class 10 Ex 10.2 Zip the line joining the point of intersection to the centre makes equal angles with the chords.

Solution: Given : Two circles with the common centre O. Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park.

If the distance between Reshma and Salma and between Salma and Mandip is 6 m each, what is the distance between Reshma and Mandip? A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other.

Find the length of the string of each phone. Let the length of each side of the equilateral triangle be 2x. A chord of a circle is equal to the radius of the circle, find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

Solution: We have a circle having a chord AB equal to radius of the circle. Solution: The angle subtended by an arc of a circle at its centre is twice the angle subtended by the same arc at a point pn the circumference. In figure, A, B and C are four points on a circle. ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. Solution: Since angles in the same segment of a circle are equal. If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.

If the non � parallel sides of a trapezium are equal, prove that it is cyclic. Two circles intersect at two points B and C. Solution: Since, angles in the same segment of a circle are equal. If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

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