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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
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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


D.

140 degree

From figure, 
          OA = OC (radii of a circle)

therefore      angle OAC space equals space angle OCA space equals space 20 degree
In increment AOC,
angle AOC space equals space 180 degree minus left parenthesis angle OAC plus angle OCA right parenthesis
(by angle sum property of a triangle)
           equals 180 degree minus left parenthesis 20 degree plus 20 degree right parenthesis
equals 180 degree minus 40 degree space equals space 140 degree
Now, reflex angle AOC space equals space 360 degree space minus space angle AOC
                           equals 360 degree minus 140 degree
equals space 220 degree
therefore           angle ABC space equals space 1 half cross times space reflex space angle AOC
                           equals 1 half cross times 220 degree space equals space 110 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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