Olympiad – Class IX – Mathematics - Circles

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Question - 1

AB is a chord of a circle with centre O and radius 17 cm. lf OM丄AB and OM = 8 cm, find the length of chord AB.

  • A 12 cm
  • B 30 cm
  • C 15 cm
  • D 24 cm

Question - 2

AB is a chord of length 24 cm of a circle with centre O and radius 13 cm. Find the distance of the chord from the centre.

  • A 5 cm
  • B 6 cm
  • C \(\sqrt{407}\) cm
  • D 25 cm

Question - 3

48 cm long chord of a circle is at a distance of 7 cm from the centre. Find the radius of the circle.

  • A 5 cm
  • B 17 cm
  • C 25 cm
  • D 16 cm

Question - 4

A chord of a circle is 12 cm in length and its distance from the centre is 8 cm. Find the length of the chord of the same circle which is at a distance of 6 cm from the centre.

  • A 30 cm
  • B 24 cm
  • C 16 cm
  • D 18 cm

Question - 5

In the given figure, ΔABC is inscribed in a circle with centre O. lf ㄥACB = 65°, find ㄥABC.

  • A 25°
  • B 35°
  • C 90°
  • D 65°

Question - 6

An equilateral ΔPQR is inscribed in a circle with centre O. Find ㄥQOR..

  • A 60°
  • B 120°
  • C 30°
  • D 90°

Question - 7

In the given figure, ΔXYZ is inscribed in a circle with centre O. If the length of the chord YZ is equal to the radius of the circle OY, find the measure of ㄥYXZ.

  • A 60°
  • B 30°
  • C 80°
  • D 100°

Question - 8

In the given figure, O is the centre of a circle. If ㄥDAC = 54° and ㄥACB = 63°, find ㄥOAB.

  • A 72°
  • B 54°
  • C 81°
  • D 27°

Question - 9

Find the value of x in the following figure.

  • A 45°
  • B 35°
  • C 60°
  • D 55°

Question - 10

What is the least number of noncollinear points required to draw a circle passing through them?

  • A Two
  • B Three
  • C Four
  • D Nine