Given below are the **Class 9 Maths** Important questions for Circles

b) Calculation problems

c) Multiple choice questions

d) Long answer questions

e) Fill in the blank's

1) ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If < DBC= 550 and < BCD.

2) In the figure O is the centre of the circle and < ABC = 450 . Show that OA is perpendicular to OC

3) Two concentric circles are with center O. ABCD are the points of intersection with a line. If AD = 12 cm and BC = 8 cm find the length of AB, CD, AC and BD

4) ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠ DBC = 70°, ∠ BAC = 30°, find ∠ BCD. Further, if AB = BC, find ∠ ECD

5) Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. Prove that the angles of the triangle DEF are 90° – (1 /2 )A, 90° – (1/ 2) B and 90° – (1 /2) C.

6) 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.

7) Two chords AB and CD of lengths 5 cm and 11 cm 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

8) . AB and AC are two chords of circle of radius r such that AB = 2AC. If p and q are the distances of AB and AC from centre, prove that 4q^{2} = p^{2} + 3r^{2}.

9) A quadrilateral PQRS is inscribed in a circle such that PQ is a diameter and <PSR = 130. Find <QPR

10) In below figure two chords AB and CD of a circle intersect at right angle. If <ABD =65, find the measure of <CAB.

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