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UNIVERSAL CLASSES, KHARGHAR, Periodic Test VI, Class : IX, Subject : Maths, Time : 60 mins, Total Marks : 20, Circles, Q1. Solve the following:, (2 × 5 = 10), 1) Two chords AB and CD of lengths 5 cm and 11cm respectively of a circle are parallel, to each other and are on opposite sides of its centre. If the distance between AB, and CD is 6 cm, find the radius of the circle., 2) 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., 3) 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., 4) In Fig alongside, ∠ PQR = 100°, where P, Q and R are points on a circle with centre, O. Find ∠ OPR., , 5) If O is the centre of the circle. Find the value of x in the following figure:, , Q2. Solve the following: (Any 2), , (3 × 2 = 6), , 1) If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices, of the quadrilateral, prove that it is a rectangle., 2) Three girls Reshma, Salma and Mandip are playing a game by standing on a circle, of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip,, Mandip to Reshma. If the distance between Reshma and Salma and between, Salma and Mandip is 6m each, what is the distance between Reshma and Mandip?

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3) In Fig, A, B, C and D are four points on a circle. AC and BD intersect at a point E, such that ∠ BEC = 130° and ∠ ECD = 20°. Find ∠ BAC., , Q3. Solve the following: (Any 1), (4 × 1 = 4), 1) If a line intersects two concentric circles (circles with the same centre) with centre, O at A, B, C and D, prove that AB = CD (see the below fig)., , 2) If the non-parallel sides of a trapezium are equal, prove that it is cyclic., , All the Best!