A, B, C are three points on a circle. The tangent at A meets BC

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 Multiple Choice QuestionsMultiple Choice Questions

1.

AC is transverse common tangent to two circles with centres P and Q and radii 6cm and 3 cm at the point A and C, respectively. If AC cuts PQ at the point B and AB = 8 cm, then the length of PQ is

  • 10 cm

  • 12 cm

  • 13 cm

  • 13 cm

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2.

PR is a tangent to a circle with centre O and radius 4 cm at point Q. If angle POR space equals space 90 degree, OR = 5 cm and OP = 20 over 3 cm comma then the length of PR is:

  • 3 cm

  • 16 over 3 cm
  • 23 over 3 cm
  • 23 over 3 cm
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3.

A chord of a circle is equal to its radius. A tangent is drawn to the circle at an extremity of the chord. The angle between the tangent and the chord is

  • 30°

  • 45°

  • 60°

  • 60°

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4.

Two circles with centres P and Q touch each other externally. A straight line drawn through the point of contact intersects the circle with centre P at A and the circle with centre Q at B. Then, which of the following is true?

  • AP = BQ

  • AP/BQ

  • AP || BQ

  • AP || BQ

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5.

PQ is a tangent to the circle at T. If TR = TS where R and S are points on the circle and ∠RST = 65°, the ∠PTS = ?

  • 65°

  • 130°

  • 115°
  • 115°
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6.

In a circle, a diameter AB and a chord PQ (which is not a diameter) intersect each other at X perpendicularly. If AX : BX = 3 : 2 and the radius of the circle is 5 cm, then the length of chord PQ is

  • 2 square root of 13 space cm
  • 5 square root of 3 space cm
  • 4 square root of 6 space cm
  • 4 square root of 6 space cm
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7.

Let P and Q be two points on a circle with centre O. If two tangents of the circle through P and Q meet at A with angle PAQ space equals space 48 degree comma space then space angle APQ is

  • 96° 

  • 48° 

  • 66° 

  • 66° 

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8.

AB is a diameter of a circle with centre O. The tangents at C meets AB produced at Q. If angle CAB space equals space 34 degree, then measure of angle CBA is

  • 56° 

  • 34° 

  • 68° 

  • 68° 

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9.

The radius of a circle is 6 cm. The distance of a point lying outside the circle from the centre is 10 cm. The length of the tangent drawn from the outside point to the circle is

  • 5 cm

  • 6 cm

  • 7 cm

  • 8 cm

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10.

A, B, C are three points on a circle. The tangent at A meets BC produced at T, angle BTA space equals space 40 degree comma space space angle CAT space equals 44 degree. The angle subtended by BC at the centre of the circle is

  • 84°

  • 92°

  • 96°

  • 96°


D.

96°



angle CAT space equals space 44 degree space left parenthesis given right parenthesis
angle BTA space equals space 40 degree space space left parenthesis given right parenthesis
angle ACT space equals space 180 degree space minus 44 degree space minus space 40 degree space equals space 96 degree
angle CAT space equals space angle CBA space equals space 44 degree space space left parenthesis Alternate space segment space theorem right parenthesis

rightwards double arrow space space angle BCA space equals space 180 degree space minus space 96 degree space equals space 84 degree
therefore space space angle BAC space equals space 180 degree space minus space 84 degree minus 44 degree space equals space 52 degree

∴  Angle subtended by BC at the centre = 2 x 52° = 104°


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