IX Circle Geometry Important questions Test paper

1.       In the figure 9.5 If O is the centre of the circle and < AOC =100. Find < ABC. Give reason.

2.       In the figure 9.6 O is the centre of the circle. Find ∠BAC?

3.       Two concentric circles with centre O have A, B, C, and D as the points of intersection with the line l as shown in the figure 9.7. If AD=12 cm, BC = 8 cm, find the lengths of AB, CD, AC and BD.

4. In the given9.8, figure two circles intersect at A and B and AC and AD respectively diameters of the circle. Prove that the points C, B and D are collinear.
5. In the given figure 9.9, find the value of x

6.       In the given figure 9.10, AB is a diameter of the circle and CD II AB. If <DAC=25⁰. Calculate (i) <ACD, (ii) <CAD

7.       In the given figure 9.11, POQ is a diameter and PQRS is a cyclic quadrilateral. If <PSR=150. Find <RPQ.

8.       If two sides of a cyclic quadrilateral are parallel, prove that its remaining two sides are equal and the diagonals are equal

9       In the figure 9.13, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If <DBC=53 and<BAC=45. Find <BCD

10   Find the length of a chord which is at a distance of 8 cm from the centre of the circle of radius 17cm.

11. Equal chords of a circle subtend equal angles at the centre

12. If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

13. Two chords of a circle intersect in the interior of the circle and make equal angles with the diameter passing through their point of intersection. prove that the chords are equal.

14. Prove that the quadrilateral formed (if possible) by the internal angle bisectors of any quadrilateral is cyclic

15.Prove 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.
Or,   Chords AB and CD intersect at P when produced. Chord BD is equal to radius .Prove <P = 60°.

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