If the length of a chord of a circle at a distance of 12cm from

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 Multiple Choice QuestionsMultiple Choice Questions

11.

Two chords AB and CD of a circle with centre O intersect at P. If ∠APC = 40°. Then the value of ∠AOC + ∠BOD is

  • 50°

  • 60°

  • 80°

  • 80°

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12.

The radii of two concentric circles are 17cm and 25 cm. A straight line PQRS intersects the larger circle at the points P and S and intersects the smaller circle at the points Q and R. If QR = 16cm, then the length (in cm.) of PS is

  • 41

  • 32

  • 33

  • 33

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13.

A is the centre of a circle whose radius is 8 and B is the centre of a circle whose diameter is 8. If these two two circles touch externally, then the area of the circle with diameter AB is

  • 36 straight pi
  • 64 straight pi
  • 144 straight pi
  • 144 straight pi
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14.

Two chords of lengths a metre and b metre subtend angles 60° and 90° at the centre of the circle respectively, which of the following is true?

  • a = √2 b

  • b = √2 a

  • a = 2b

  • b = 2a

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15.

Two chords AB and CD of a circle with centre O. Intersect each other at P. If ∠AOD = 100° and ∠BOC = 70°, then the value of ∠APC is

  • 80°

  • 75°

  • 85°

  • 85°

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16.

If two concentric circles are of radii 5cm and 3cm, then the length of the chord of the larger circle which touches the smaller circle is

  • 6 cm

  • 7 cm

  • 10 cm

  • 10 cm

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17.

Let C be a point on a straight line AB. Circles are drawn with diameters AC and AB. Let P be any point on the circumference of the circle with diameter AB. If AP meets the other circle at Q, then

  • QC || PB

  • QC is never parallel to PB

  • QC space equals space 1 half PB
  • QC space equals space 1 half PB
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18.

IF I is the incentre of ΔABC and angle BIC space equals space 135 degree, then ΔABC is 

  • acute angled

  • equilateral

  • right angled

  • right angled

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19.

If the length of a chord of a circle at a distance of 12cm from the centre is 10 cm, then the diameter of the circle is

  • 13 cm

  • 15 cm

  • 26 cm

  • 26 cm


C.

26 cm


OC = 12 cm,
AC = CB = 5 cm (Line drawn through the centre of a circle bisects a chord. 
∴ Radius OA space equals space square root of OC squared space plus space AC squared end root
   equals space square root of left parenthesis 12 right parenthesis squared space plus space left parenthesis 5 right parenthesis squared end root space equals space square root of 144 space plus space 25 end root space equals space square root of 169 space equals space 13 space cm
∴  Diameter of a circle  = 2 x 13 = 26 cm

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20.

If O is the circumcentre of ΔABC and angle OBC space equals space 35 degree, then the angle BAC is equal to

  • 55°

  • 110°

  • 70°

  • 70°

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