Mathematics · Quantitative Aptitude

Circle Geometry

232 Questions

Circle geometry focuses on the properties and dimensions of circles, including radius, diameter, circumference, and area calculations. Questions often involve concentric circles, sectors, and inscribed shapes. This topic frequently appears in quantitative aptitude sections of major competitive exams.

Area and circumferenceConcentric circlesCircle sectorsInscribed polygonsSemicircle area

Circle Geometry Questions

Multiple choice

A circle has an area of 36π square units. What is the length of its radius?

  1. 3 units

  2. 4 units

  3. 5 units

  4. 6 units
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The area of a circle is given by (A = πr^2), where r is the radius. If the area is 36π square units, then the radius is 6 units.

Multiple choice

What is the circumference of a circle with a diameter of 14 cm?

  1. 14π cm

  2. 22π cm

  3. 28π cm

  4. 44π cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The circumference of a circle is given by (C = πd), where d is the diameter. If the diameter is 14 cm, then the circumference is 22π cm.

Multiple choice

What is the area of the sector of a circle with radius 12 cm and central angle 60 degrees?

  1. 18π cm^2

  2. 36π cm^2

  3. 54π cm^2

  4. 72π cm^2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area of a sector of a circle is given by (A = \frac{θ}{360}πr^2), where θ is the central angle in degrees, r is the radius, and π is the constant pi. If the radius is 12 cm and the central angle is 60 degrees, then the area of the sector is 36π cm^2.

Multiple choice

What is the area of a circle with radius 5?

  1. 25π

  2. 50π

  3. 75π

  4. 100π
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a circle is given by the formula $A = πr^2$. Substituting the given value, we get $A = π(5)^2 = 25π$.

Multiple choice

What is the area of a sector of a circle with radius 10 and central angle 60 degrees?

  1. 25π

  2. 50π

  3. 75π

  4. 100π
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a sector of a circle is given by the formula $A = (θ/360)πr^2$, where θ is the central angle in degrees and r is the radius of the circle. Substituting the given values, we get $A = (60/360)π(10)^2 = (1/6)π(100) = 25π$.

Multiple choice

A circle has a radius of 10 centimeters. What is the circumference of the circle in centimeters?

  1. 20π

  2. 30π

  3. 40π

  4. 50π
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The circumference of a circle is given by the formula: C = 2πr, where r is the radius of the circle. Therefore, the circumference of the circle is 2π * 10 = 20π centimeters.

Multiple choice

What is the name of the theorem that states that the area of a circle is equal to pi times the square of its radius?

  1. Pythagorean theorem

  2. Brahmagupta theorem

  3. Angle sum theorem

  4. Area of a circle formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The area of a circle formula states that the area of a circle is equal to pi times the square of its radius.

Multiple choice

What is the area of a circle with radius 5 cm?

  1. 25π cm^2

  2. 50π cm^2

  3. 75π cm^2

  4. 100π cm^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a circle is given by the formula πr^2. Therefore, the area of a circle with radius 5 cm is π(5)^2 = 25π cm^2.

Multiple choice

What is the name of the theorem that states that the angle formed by a tangent and a chord at the point of contact is equal to the angle formed by the chord and the diameter passing through the point of contact?

  1. Thales' theorem

  2. Pythagoras' theorem

  3. Euler's theorem

  4. Bhaskara's theorem
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Bhaskara's theorem is a fundamental result in the geometry of circles that establishes a relationship between the angles formed by a tangent, a chord, and a diameter.

Multiple choice

What is the name of the theorem that states that the product of the lengths of the tangents drawn from a point outside a circle to the circle is equal to the square of the distance from the point to the center of the circle?

  1. Pythagoras' theorem

  2. Euler's theorem

  3. Descartes' theorem

  4. Menelaus' theorem
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Descartes' theorem is a significant result in the geometry of circles that establishes a relationship between the lengths of tangents drawn from a point outside a circle and the distance from the point to the center of the circle.

Multiple choice

What is the name of the theorem that states that the angle formed by a tangent and a chord at the point of contact is equal to half the angle formed by the chord and the diameter passing through the point of contact?

  1. Thales' theorem

  2. Pythagoras' theorem

  3. Euler's theorem

  4. Bhaskara's theorem
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Thales' theorem is a fundamental result in the geometry of circles that establishes a relationship between the angles formed by a tangent, a chord, and a diameter.

Multiple choice

What is the name of the theorem that states that the angle formed by a tangent and a chord at the point of contact is equal to the angle formed by the chord and the diameter passing through the point of contact?

  1. Thales' theorem

  2. Pythagoras' theorem

  3. Euler's theorem

  4. Bhaskara's theorem
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Thales' theorem is a fundamental result in the geometry of circles that establishes a relationship between the angles formed by a tangent, a chord, and a diameter.

Multiple choice

What is the name of the theorem that states that the area of a circle is equal to pi times the square of its radius?

  1. Pythagorean Theorem

  2. Brahmagupta's Theorem

  3. Euclid's Theorem

  4. Area of a Circle Formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Area of a Circle Formula is a well-known formula for finding the area of a circle.

Multiple choice

What is the name of the theorem that states that the circumference of a circle is equal to 2 pi times its radius?

  1. Pythagorean Theorem

  2. Brahmagupta's Theorem

  3. Euclid's Theorem

  4. Circumference of a Circle Formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Circumference of a Circle Formula is a well-known formula for finding the circumference of a circle.

Multiple choice

What is the name of the theorem that states that the area of a circle is equal to pi times the square of its radius?

  1. Pythagorean Theorem

  2. Brahmagupta's Theorem

  3. Euclid's Theorem

  4. Area of a Circle Formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Area of a Circle Formula is a well-known formula for finding the area of a circle.