If O is the circumcentre of ΔABC and , then the  is equal t

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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

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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°


A.

55°



OB = OC = radius
 therefore space space space space space space space space space space angle OBC space equals space angle OCB space equals space 35 degree
therefore space space space space space space space space space angle BOC space equals space 180 degree space minus space 70 degree space equals space 110 degree
therefore space space space space space space space space space angle BAC space equals space 55 degree

The angle subtended at the centre by an arc is twice to the angle subtended at the circumference.


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