### 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