Scholastic Aptitude Test - Mathematics - Circles

Question - 1

The distance between two points A and B is 3 em. A  circle of radius 1.7 cm is drawn to pass through those points. Find the distance of AB from the centre of the circle

  • A 0.64
  • B \(\sqrt { 0.64 } \)
  • C 0.8cm
  • D 0.08 cm

Question - 2

A circular dice of radius 6 em is divided into three sectors with central angles 90°, 120° and 150°. What part of the whole circle is the sector with central angle 150"? Calculate the ratio of the areas of the three sectors.

  • A 2:3:4
  • B 4:5:6
  • C 1:2:3
  • D 3:4:5

Question - 3

In a circle of radius 10.5 cm, the minor arc is \(\frac { 1 }{ 5 } \) th of the major arc. Find the area of the sector corresponding to the major arc.

  • A 287 cm2
  • B 286 cm2
  • C 276 cm2
  • D 288.75 cm2

Question - 4

In the adjoining figure, OPQR is a rhombus, three of whose vertices lie on a circle with centre O. If the area of the rhombus is 32 \(\sqrt { 3 } \) cm2, Find the radius of the circle

  • A 5 cm
  • B 6 cm
  • C 8 cm
  • D none of these

Question - 5

In the given figure, ABC is right angled at A, with AB=6 cm, AC=8 cm, A circle with centre 0 has been inscribed inside the triangle. Find the .value of r, the radius of the inscribed circle.

  • A 1 cm
  • B 2 cm
  • C 3 cm
  • D none of these

Question - 6

The distance between the centre of the two circles with radii 4 cm and 9 cm is 13 cm. The length of the direct common tangent (between two points of contact) is

  • A 13 cm
  • B \(\sqrt { 153 } cm\)
  • C 12 cm
  • D 18 cm

Question - 7

AB is a diameter of a circle with centre at O. DC is a chord of it such that DC II AB. If = 20o, then is equal to

  • A 120o
  • B 110o
  • C 115o
  • D 100o

Question - 8

Two chords AB and CD of circle whose circle is 0, meet at the point P and  = 50o,  = 40o.Then the  value of  is

  • A 60o
  • B 40o
  • C 45o
  • D 75o

Question - 9

One chord of a circle is known to be lO.lcm. The radius of this circle must be

  • A 5 cm
  • B Greater than 5 cm
  • C greater than or equal to 5 cm
  • D Less than 5 cm

Question - 10

From four corners of a square sheet of side 4cm, four pieces, each in the shape of arc of a circle with radius 2cm are cut out. The area of the remaining portion is

  • A (8 -\(\pi \)  )sq.cm
  • B (16- 4\(\pi \)) sq.cm
  • C (16- 8\(\pi \)) sq.cm
  • D (4- 2\(\pi \)) sq.cm
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