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SSC SI CAPF Exam Quantitative Aptitude Study Material

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Circles

Let C₁ and C₂ be the inscribed and circumscribed circles of a triangle with sides 3 cm, 4 cm , and 5 cm then is area ofC₁ is area of C₂

a) 9/16
b) 9/25
c) 4/25
d) 16/25

✔Answer

✔Solution

Correct Answer Is : 4/25

Solution Is : Here the side of triangle are 3,4and 5.
So,triangle is right angle triangle.
When triangle is circumscribed (C1).
Radius of circle = 5/2.
When triangle is Inscribed(C2). (figure 2)
Let BE=x , Then DE =x(triangle)
CE=4-x ;
AC=3-x+4-x
5=7-2x ⇒ x=1.
Now , (Area of C1/Area of C2) =πr1²/ πr2² [π(1)²/π(5/2)²] =4/25.

XY and XZ are tangents to a circle, ST is another tangent to the circle at the point R on the circle, which intersects XY and XZ at S and T respectively. If XY = 15 cm and TX = 9 cm, then RT is

a) 4.5 cm
b) 7.5 cm
c) 6 cm
d) 3 cm

✔Answer

✔Solution

Correct Answer Is : 6 cm

Solution Is :

ABC is a cyclic triangle and the bisectors of ∠BAC, ∠ABC and ∠BCA meet the circle at P, Q, and R respectively. Then the angle ∠RQP is

a) 90° - B/2
b) 90° + B/2
c) 90° + C/2
d) 90° - A/2

✔Answer

✔Solution

Correct Answer Is : 90° - B/2

Solution Is :

Two circles touch each other externally. The sum of their areas is 130 it sq cm and the distance between their centres is 14 cm. The radius of the smaller circle is

a) 2cm
b) 4cm
c) 5cm
d) 3cm

✔Answer

✔Solution

Correct Answer Is : 3cm

Solution Is :

The tangents drawn at the points A and B of a circle centred at 0 meet at P. If ∠AOB = 120° then ∠APB : ∠APO is :

a) 2 : 5
b) 3 : 2
c) 4 : 1
d) 2 : 1

✔Answer

✔Solution

Correct Answer Is : 2 : 1

Solution Is :

P and Q are the middle points of two chords (not diameters) AB and AC respectively of a circle with centre at a point 0. The lines OP and OQ are produced to meet the cirle respectively at the points R and S. T is any point on the major arc between the points R and S of the circle. If ∠BAC = 32°, ∠RTS = ?

a) 32°
b) 74°
c) 106°
d) 64°

✔Answer

✔Solution

Correct Answer Is : 74°

Solution Is :

Two equal circles pass through each other`s centre. If the radius of each cirlce is 5 cm, what is the length of the common chord?

a) 5
b) 5√3
c) 10√3
d) 5√3 / 2

✔Answer

✔Solution

Correct Answer Is : 5√3

Solution Is :

The diameter of a garden roller is 1.4 metre and it is 2 metre long. The area covered by the roller in 5 revolutions is :

a) 8.8 m²
b) 4.4 m²
c) 44 m²
d) 16.8 m²

✔Answer

✔Solution

Correct Answer Is : 44 m²

Solution Is : (3) Area covered in 1 revolution
=2πrl
=(2×22/7×0.7×2)sq.metre
=8.8 sq.metre Therefore,Area covered in 5 revolutions=5*8.8=44 sq.metre.

In the following figure, 0 is the centre of the circle and XO is perpendicular to OY. If the area of the triangle XOY is 32, then the area of the circle is

a) 64 π
b) 256 π
c) 16 π
d) 32 π

✔Answer

✔Solution

Correct Answer Is : 64 π

Solution Is :

Two tangents are drawn from a point P to a circle at A and B. 0 is the centre of the circle. If ∠AOP = 60°. then ∠APB is

a) 120°
b) 90°
c) 60°
d) 30°

✔Answer

✔Solution

Correct Answer Is : 60°

Solution Is :

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SSC SI CAPF Exam Quantitative Aptitude Study Material

Circles

Let C1 and C2 be the inscribed and circumscribed circles of a triangle with sides 3 cm, 4 cm , and 5 cm then is area ofC1 is area of C2

Correct Answer Is : 4/25

XY and XZ are tangents to a circle, ST is another tangent to the circle at the point R on the circle, which intersects XY and XZ at S and T respectively. If XY = 15 cm and TX = 9 cm, then RT is

Correct Answer Is : 6 cm

Solution Is :

ABC is a cyclic triangle and the bisectors of ∠BAC, ∠ABC and ∠BCA meet the circle at P, Q, and R respectively. Then the angle ∠RQP is

Correct Answer Is : 90° - B/2

Solution Is :

Two circles touch each other externally. The sum of their areas is 130 it sq cm and the distance between their centres is 14 cm. The radius of the smaller circle is

Correct Answer Is : 3cm

Solution Is :

The tangents drawn at the points A and B of a circle centred at 0 meet at P. If ∠AOB = 120° then ∠APB : ∠APO is :

Correct Answer Is : 2 : 1

Solution Is :

Correct Answer Is : 74°

Solution Is :

Two equal circles pass through each other`s centre. If the radius of each cirlce is 5 cm, what is the length of the common chord?

Correct Answer Is : 5√3

Solution Is :

The diameter of a garden roller is 1.4 metre and it is 2 metre long. The area covered by the roller in 5 revolutions is :

Correct Answer Is : 44 m2

Solution Is : (3) Area covered in 1 revolution =2πrl =(2×22/7×0.7×2)sq.metre =8.8 sq.metre Therefore,Area covered in 5 revolutions=5*8.8=44 sq.metre.

In the following figure, 0 is the centre of the circle and XO is perpendicular to OY. If the area of the triangle XOY is 32, then the area of the circle is

Correct Answer Is : 64 π

Solution Is :

Two tangents are drawn from a point P to a circle at A and B. 0 is the centre of the circle. If ∠AOP = 60°. then ∠APB is

Correct Answer Is : 60°

Solution Is :

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Let C₁ and C₂ be the inscribed and circumscribed circles of a triangle with sides 3 cm, 4 cm , and 5 cm then is area ofC₁ is area of C₂

Correct Answer Is : 44 m²

Solution Is : (3) Area covered in 1 revolution
=2πrl
=(2×22/7×0.7×2)sq.metre
=8.8 sq.metre Therefore,Area covered in 5 revolutions=5*8.8=44 sq.metre.