Mathematics · Quantitative Aptitude

Circle and Arc Properties

115 Questions

Circle and arc properties involve calculating arc lengths, understanding radius relationships, and solving geometric proofs. These geometry concepts are crucial for quantitative aptitude tests. Review these questions to improve your spatial reasoning and accuracy.

Arc length calculationsCircle theoremsRadius and diameterInscribed polygonsCentral angles

Circle and Arc Properties Questions

Multiple choice general knowledge math & puzzles

In which type of geometry is pi the ratio of a circle’s circumference to its diameter?

  1. Pythagorean

  2. Archimedian

  3. Euclidean

  4. Galilean
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In Euclidean geometry, π is defined as the ratio of a circle's circumference to its diameter. Euclidean geometry is the classical form of geometry based on Euclid's axioms. In non-Euclidean geometries (spherical or hyperbolic), the ratio of circumference to diameter is not constant and differs from π. This is a fundamental property that distinguishes Euclidean from other geometric systems.

Multiple choice general knowledge science & technology

What is the arc length of a segment having included angle theta in radians and radius “R”?

  1. 2 pi R Theta

  2. R x R x Theta

  3. R x theta/ (2 pi)

  4. R x theta
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The formula for arc length when angle is in radians is s = R × theta, where theta is the angle in radians. This is because the definition of radian measure comes from arc length divided by radius. Option A would give circumference multiplied by angle, while option B incorrectly squares the radius.

Multiple choice general knowledge math & puzzles

Three circles touch each other externally. If xy = 15 ,yz = 10, xz = 21 Find the radius of each circle.

  1. 13 ,8 ,2

  2. 14 , 5 ,9

  3. 10 ,13 ,12

  4. 5 ,6 ,3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the radii be a, b, and c. The distances between centers are sums of radii: a+b=15, b+c=10, and a+c=21. Adding these gives 2(a+b+c)=46, so a+b+c=23. Solving for each: c=23-15=8, a=23-10=13, and b=23-21=2. The radii are 13, 8, and 2.

Multiple choice general knowledge math & puzzles

In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?

  1. 26.25

  2. 27.85

  3. 22.45

  4. 32.25
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the right triangles ABD and ACD, we find BC = BD + DC. From Pythagoras: BD = sqrt(17.5^2 - 3^2) and DC = sqrt(9^2 - 3^2). This gives BC ≈ 25.725. The circumradius formula R = abc/(4 × Area) with Area = (1/2) × BC × AD yields R = (17.5 × 9 × 25.725)/(4 × 38.588) ≈ 26.25.

Multiple choice general knowledge math & puzzles

If an angle inscribed in a circle is bisected, the bisection ray passes through the center.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

An angle inscribed in a circle is bisected by a ray. This ray only passes through the center of the circle if the inscribed angle is symmetric with respect to the center (i.e., its sides are chords of equal length). In general, it does not pass through the center, so the statement is false.

Multiple choice maths area of complex plane figures 2d and 3d figures

A pentagon is made up of an equilateral $\triangle ABC$ of side length $2cm$ on top of a square $BCDE$. Circumscribe a circle through points, $A, D$ and $E$. The radius of the circle is

  1. $1+\dfrac {\sqrt {3}}{2}$
  2. $5-2\sqrt {3}$
  3. $2$
  4. $1+\sqrt {3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The geometry involves a square and an equilateral triangle. Calculating the circumradius of the points A, D, and E requires coordinate geometry or circle properties. The correct radius is 5 - 2*sqrt(3).