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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


A.

13

Let the radius of circle be r cm.

AB = 10 cm and CD = 24 cm
In increment ONA,        left parenthesis OA right parenthesis squared space equals space left parenthesis ON right parenthesis squared plus space left parenthesis AN right parenthesis squared space space 
                         straight r squared space equals space left parenthesis ON right parenthesis squared space plus space left parenthesis 5 right parenthesis squared
                     ...(i)
In increment OMC comma         left parenthesis OC right parenthesis squared equals space space left parenthesis OM right parenthesis squared space plus space left parenthesis 12 right parenthesis squared
                          straight r squared space equals space left parenthesis 17 minus ON right parenthesis squared space plus space left parenthesis 12 right parenthesis squared           ...(ii)
Solving Eqs. (i) and (ii),
                          straight O space equals space left parenthesis 17 minus ON right parenthesis squared minus left parenthesis ON right parenthesis squared plus left parenthesis 12 right parenthesis squared minus left parenthesis 5 right parenthesis squared
rightwards double arrow               289 plus left parenthesis ON right parenthesis squared space minus 34 left parenthesis ON right parenthesis minus left parenthesis ON right parenthesis squared plus 44 minus 25 space equals space 0
rightwards double arrow                289 plus 144 minus 25 space equals space 34 space cross times space ON
therefore                                     ON space equals space 408 over 34 space equals space 12 space cm
From Eq. (i),  straight r squared space equals space left parenthesis 12 right parenthesis squared plus space left parenthesis 5 right parenthesis squared space equals space 144 plus 25 space equals space 169
therefore                    r = 13 cm
                          

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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
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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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