In the given figure, O is the centre, Then x, is equal to from

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 Multiple Choice QuestionsMultiple Choice Questions

1.

O is the circumcentre of . If , then  is equal to

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2.

If discount of 10% is given on the marked price of a radio, the gain is 20%. If the discount is increased to 20%, the gain is

  • 5%

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3.

O is the centre of  and , then the measure of  is

  • 125°

  • 100°

  • 130°

  • 115°

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4.

AB and CD are two parallel chords of a circle lying on the opposite side of the centre and the distance between them is 17cm. The length of AB and CD are 10 cm and 24 cm, respectively. The radius (in cm) of the circle is

  • 13

  • 9

  • 18

  • 18

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5.

In the given figure, O is the centre, Then x, is equal to

  • 45 degree
  • 55 degree
  • 65 degree
  • 65 degree


B.

55 degree

Joint P to O.

OP = OQ (radii)
therefore space space angle OPQ space equals space angle OQP space equals space 35 degree
We know that the angle subtended by an arc of a circle at the centre is twice the angle subtended by it at any point on the remaining part of the circle.
In increment POQ,
     angle OPQ plus angle OQP plus angle POQ space equals space 180 degree        
            (angle sum property of a triangle)
 rightwards double arrow space 35 degree space plus space 35 degree space plus space angle POQ space equals space 180 degree
rightwards double arrow space space space space space space space space space space space space space space space space space space space space angle POQ space equals space 180 degree minus 70 degree
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 110 degree
Therefore,         angle POQ space equals space 2 angle PRQ
rightwards double arrow              angle PRQ space equals space 1 half cross times 110 degree space equals space 55 degree

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6.

AC is a chord of circle whose centre is at O. If B is any point on the arc AC and angle OCA space equals space 20 degree, then the magnitude of  angle ABC is

  • 100 degree
  • 40 degree
  • 140 degree
  • 140 degree
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7.

Two equal arcs of the two circles subtend angle of 60 degree and 75 degree at the centre. The ratio of the radii of the two circles is

  • 5 over 4
  • 3 over 2
  • 4 over 5
  • 4 over 5
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8.

An angle in a semicircle is 

  • 45 degree
  • 60 degree
  • 90 degree
  • 90 degree
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9.

A chord of length 16 cm is drawn in a circle of radius 10 cm. The distance of the chord from the centre of the circle is

  • 8 cm

  • 6 cm

  • 4 cm

  • 12 cm

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10.

In a circle with centre O, AB is a diameter and CD is a chord which is equal to the radius OC. AC and BD are extended in such a way that they intersect each other at a point P, exterior to the circle. The measure of ∠APB is

  • 30°

  • 45°

  • 60°

  • 60°

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