Olympiad – Class X – Mathematics - Circles

Buy Olympiad -X Standard Practice test pack

Question - 1

PT is a tangent and PAB is a secant of the circle meeting the circle at A and B. If PA = 4 cm and AB = 5 cm. What is the length of PT?

  • A 8 cm
  • B 6 cm
  • C 3 cm
  • D 1 cm

Question - 2

In the given figure, AB is a tangent at P.

Find  \(\angle APD.\)

  • A \(\angle PDE\)
  • B \(\angle EPB\)
  • C \(\angle DPE\)
  • D \(\angle PED\)

Question - 3

Two concentric circle have their centres at O. OP = 4 cm and OQ = 5 cm. AB is a chord of the circle and a tangent to the inner circle at P.

Find the length of AB.

  • A 6 cm
  • B 5 cm
  • C 8 cm
  • D 9 cm

Question - 4

Find the value of x.

  • A \({5\over 2}\)
  • B \({8\over 3}\)
  • C \({6\over 5}\)
  • D \({9\over 4}\)

Question - 5

What is the number of common tangents that can be drawn to two intersecting circles touching at two points?

  • A 2
  • B 4
  • C 3
  • D 1

Question - 6

If the four sides of a quadrilateral ABCD are tangential to a circle, which of the following is true?

  • A AC + AD = BD + CD
  • B AB + CD = BC+ AD
  • C AB + CD = AC + BD
  • D AC + AD = BC+ AB

Question - 7

In the given figure, OA and OB are two radii of the circle.lfPA and PB are tangents to the circle at A and B respectively which is the correct statement?

  • A \(\angle AOB\)  and \(\angle APB\)  are the supplementary angles.
  • B \(\angle PBO\) and \(\angle APB\) are complementary angles.
  • C \(\angle PBO\) and \(\angle AOB\) are complementary angles.
  • D Both (A) and (C)

Question - 8

AP is a secant and PT is a tangent to a circle. If PT= 15 cm and AB = 8BP, find AP.

  • A 45 cm
  • B 36 cm
  • C 25 cm
  • D 62 cm

Question - 9

In the figure, find \(\angle ABC\)

  • A 60°
  • B 120°
  • C 180°
  • D 90°

Question - 10

If OA and OB are radii and PA and PB are tangents to the circle, which of the following is quadrilateral OAPB?

  • A Rectangle
  • B Square
  • C Parallelogram
  • D Kite
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next