Two equal arcs of the two circles subtend angle of  and  at

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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
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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


A.

5 over 4

Length of arc of first circle  = fraction numerator 2 πr subscript 1 straight theta subscript 1 over denominator 360 degree end fraction
Lenght of arc of second circle = fraction numerator 2 πr subscript 2 straight theta subscript 2 over denominator 360 degree end fraction
According to the question,
                    fraction numerator 2 πr subscript 1 straight theta subscript 1 over denominator 360 degree end fraction space equals space fraction numerator 2 πr subscript 2 straight theta subscript 2 over denominator 360 degree end fraction
straight r subscript 1 over straight r subscript 2 space equals space straight theta subscript 2 over straight theta subscript 1 space equals space 75 over 60
straight r subscript 1 over straight r subscript 2 space equals space 5 over 4

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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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