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NCERT Solutions for Class 9 Maths (Updated for ) Aug 13, �� Theorem The perpendicular from the center of a circle to a chord bisects the chord. Given: C is a circle with center at O. AB is a chord such that OX ? AB To Prove: OX bisect chord AB i.e. AX = BX Proof: In ?OAX & ?OBX ?OXA = ?OXB OA = OB OX = OX ?. NCERT Solutions for Class 9 Maths Chapter 10 Circles are provided here in PDF format, which can be downloaded for free. The Solutions for the chapter Circles have been designed by our expert teachers as per the CBSE curriculum (), with percent accuracy. All the solved questions of Chapter 10 Circles, are with respect to NCERT syllabus and guidelines, to help students solve each exercise . Ex Class 9 Maths Question 2. Write True or False. Give reason for your answers. (i) Line segment joining the centre to any point on the circle is a, radius of the circle. (ii) A circle has only finite number of equal chords. (iii) If a circle is divided into three equal arcs, each is a major arc.
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Students report learning more Ncert Solutions Class 10th Maths Chapter 5 Login easily with TeachLearnWeb. There are hundreds of exercise items with fully worked-out solutions and explanations. Each video topic has corresponding exercises to test your understanding.

Test your understanding with hundreds of exercises that are automatically graded. Your results are available immediately, including fully worked-out solutions and explanations for each exercise. You can work on the exercises at the computer or print them out to work on later. Access your cumulative results anytime. We also offer concise, illustrated review notes, a glossary, transcripts of the video lectures, and links to relevant websites.

All of these materials may be viewed online, and the notes and transcripts may be printed and kept for reference. Join Now. Log In. Password Password Missing. 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 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 Ch 10 Maths Class 9 Theorems Image 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 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. They intersect at a point D, other than A.

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