Problems On Circles

A circle is a two-dimensional figure made up of points that are next to one another and equidistant from a fixed point. The center of the circle is the fixed point in this curved plane figure, the radius is the common distance between the points from the center, and the diameter is a line that crosses from the center of the circle starting from one point to the other. The inside of a circle, the exterior of a circle, and on the circle are the three primary sections of a circle. However, before going to the problems on circles it is important to know a few terms that will help to solve problems on circles questions.

Parts of a circle:

Circumference:

A circle’s circumference is its boundary or the length of the circle’s completion. In other words, the circumference is the measurement of the circle’s perimeter or distance around it in units of length such as centimeters, meters, or kilometers.

Diameter:

A circle’s diameter is a line segment that crosses through the center of the circle and has endpoints on the circumference of the circle. The diameter is double the radius and is also known as the circle’s longest chord.

Radius:

The radius of a circle is the length of the line segment that connects the circle’s center to any point on its circumference. Many radii can be found on a circle, and they all measure the same. The radius of a circle is usually symbolized by the letter ‘r.’

Chord of the circle:

A circle’s chord is a line segment that connects two points on the circle’s circumference. A chord divides a circle into two parts known as segments of the circle, which can be further divided into minor and major segments based on the chord’s coverage area.

Secant:

A circle’s secant is a line that cuts across the circle and intersects it at two unique points. A chord is a line segment whose ends are on the curved part of the circle, whereas a secant is a line segment that travels through the circle, making a chord or diameter of the circle.

Tangent:

A tangent to a circle is a straight line that only meets the curve of the circle at one place and does not enter the interior of the circle. The tangent makes a right angle contact with the radius of the circle. The slope and a point on the line are the two most important aspects to remember while working with tangents.

Arc:

The arc of a circle is the curved part of the circle’s circumference. In other terms, an arc is a mathematical term for the curved section of an object. A circle’s arc has two parts: a minor arc and a major arc. We must determine the length of the arc as well as the angle held by the arc of any two points to determine the measure of these arcs.

Segment:

A circle segment is defined as the area enclosed by an arc and a chord of the circle. Minor and major segments are the two sorts of segments. A minor arc of the circle creates a minor segment, and a major arc of the circle creates a major segment.

Formulas required to solve problems on circles questions:

·  Diameter (D) of a Circle:

D = 2 x r

Where r = radius of the circle 

·  Circumference (C) of a Circle:

C = 2 x π x r

Area (A) of a Circle:

π x r²

The perimeter of a Circle:

2 x π x r

·  Arc of a semicircle:

( π x r²) / 2

The perimeter of a semicircle:

π x r + 2 x r = ( π + 2)r

Problems with Circles questions:

(I)Find the area of the circular conference hall whose radius is equal to 200m.

Area of a Circle = π × r2

= π × 2002

= π × 40000

Answer:  The area of the circular conference hall is 40000π m2.

(II)The radius of a circular paper is 8in. Calculate the circumference of the circle.

The perimeter of the circle formula = 2 x π x r

C = 2 × (22/7) × (8)

Answer:  The circumference of a circular paper is 50.28 inches.

(III)When the diameter of a circular figure is 9 cm, find the radius, area, and perimeter.

 Diameter = 9 cm

Therefore, radius = 9/2

= 4.5 cm

Area = π x r²

3.14 x 4.5 x 4.5

=63.585 cm sq.

The perimeter of a circle= 2 x π x r

2 x 3.14 x 4.5

= 28.26 cm

Answer:  Radius= 4.5 cm

Area= 63.585 cm sq.

Perimeter = 28.26 cm

(IV) Sam ordered a circular cake on his birthday. Each piece of the cake was 15 cm in length.

Calculate the area of the cake that Sam ordered. You can assume that the length of the cake piece is equal to the cakes’ radius.

Solution:

We can use the area of a circle formula to calculate the area of the cake since it is circular.

Radius = 15 cm

Area of Circle  = π x r2 

= 3.14 × 15 × 15

= 706.5

Area of the cake = 706.5 cm sq.

Answer: The area of the cake ordered by Sam is 705.5cm sq.

Conclusion:

A circle is a two-dimensional shape created by forming a curve from the center that is the same distance all the way around. Circumference, radius, diameter, sector areas, chords, tangents, and semicircles are all parts of a circle. Only a handful of problems on circles questions require straight lines, so it’s important to be familiar with the formulas and units of measurement for each. A circle is a form in which all of its points are at the same distance from the center. The center of a circle is given its name. Because its center is at point A, the circle to the right is named circle A. A wheel, a dinner plate, and a coin are all instances of circles in the real world.