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Constructions (Circles) Solutions for ICSE Board Class 10 Mathematics

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Last updated date: 29th May 2024
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Constructions (Circles) Solutions for ICSE Board Class 10 Mathematics (Concise - Selina Publishers)

Free download of step-by-step solutions for class 10 mathematics chapter 19 - Constructions (Circles) of ICSE Board (Concise - Selina Publishers). All exercise questions are solved & explained by an expert teacher and as per ICSE board guidelines.


A circle is a closed curve that is constructed by connecting all points in a plane that are at a constant distance from a fixed point in the same plane. Everywhere we look, there are circles. Circular items we meet daily include a ball, a pizza, a pie, a wheel, a plate, a coin, and so on. By stringing the ends of two pencils together, we can construct a circle. Place one pencil in the middle, then run the other along the line. Finally, we have a circle.

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The Properties of Circle are

  • If the radii of two circles are equal, they are said to be congruent.

  • A circle's diameter is equal to the length of its longest chord.

  • Right at the center of the circle, equal chords subtend equal angles.

  • The cord is cut by the radius drawn perpendicular to it.

  • Circles of varying radius are similar.

  • A rectangle, trapezium, triangle, square, or kite can all be circumscribed by a circle.

  • Inside a square, triangle, or kite, a circle can be engraved.

  • The length of the chords that are equidistant from the center are the same.

  • The distance between the circle's center and the longest chord (diameter) is zero.

  • When the chord length is increased, the perpendicular distance from the circle's center decreases.

  • The tangents are parallel to each other if they get drawn at the end of the diameter.

  • The radii connecting the ends of a chord to the center of a circle form an isosceles triangle.

FAQs on Constructions (Circles) Solutions for ICSE Board Class 10 Mathematics

1. Give a brief history of the circle?

Since before the beginning of recorded history, the circle has been known. Natural circles such as the Moon, Sun, and a short plant stalk blowing in the wind over sand, which produces a circle shape in the sand, would have been seen. The circle is the foundation for the wheel, which, together with related developments like gears, allows for much of contemporary machinery. The study of the circle has influenced the development of geometry, astronomy, and calculus in the subject of mathematics.

2. What are the cyclic properties of a circle?

The word "cyclic" is derived from the Ancient Greek word "Kuklos," which means "wheel" or "circle." A cyclic quadrilateral, also known as an inscribed quadrilateral, has all of its vertices on a single circle. The vertices of this circle are said to be concyclic, and it is called the circumcircle or circumscribed circle. 

  • The Cyclic properties of Circle are:

    • When a quadrilateral is inscribed in a circle, its vertices are on the circumference of the circle, the quadrilateral is referred to as a cyclic quadrilateral.

    • Concyclic points are points that are on the circumference of the same circle.

3. What are the properties of a tangent?

The following are the properties of a tangent are:

  • A tangent to the circle is a line drawn perpendicular to a radius and passing through the end point of the radius located on the circle.

  • A line formed perpendicular to a tangent across a circle's point of contact travels through the circle's center.

  • From any point outside the circle, two tangents may always be drawn to the circle, and these tangents are of equal length.

  • The angles BOA and BPA are extra if a tangent at A and a tangent at B intersect at the exterior point P, indicating the center as O.

  • DAQ = 1 / 2 arc, i.e, if AD is tangent to the circle at A and AQ is a chord of the circle (AQ).

To know more about the topic, click here.

4. What is a Chord?

A chord is a piece of a line that connects any two points on a circle. The endpoints of these line segments are located on the circle's circumference. The Chord that passes through the center of the circle is known as the Diameter. In a circle, it is the longest chord imaginable. The word "chord" comes from the Latin word "Chorda," which means "bowstring." T A circle segment is the area that lies between the Chord and one of the Arcs. You're already familiar with the terms arc and circumference. Let's have a look at some theorems about circle chords.

5. How to prepare for the construction of circles?

It is imperative to have strong fundamentals about circles and their construction Regarding their properties and basics like radius, diameter and circumference. Moving on, you should be thorough about concepts like tangents, intersections and chords to ace the topic of constructions of circles. It is always important to practice striving towards perfection. So, practice a lot through sample papers. Try every different type of question so that you can ace the topic. 


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