What is the longest chord of a Circle? (original) (raw)
Last Updated : 23 Jul, 2025
Geometry Overview
Geometry is the major part of mathematics that deals with lines, angles, points, etc. They are the visual study of shapes and sizes. The geometric approach is seen everywhere around us as every object has a certain shape whose parameters can be studied with the help of geometrical formulas.
The article also discusses a certain change circle, with details about points lines, and chords. It also answers the question of which is the longest chord. The article is also composed of some sample problems of diameter along with their solutions.
Points
A point is a geometric location represented by a dot (.) on the plane surface. a point does not have any dimensions. It does not comprise length, breadth, or height. But, all the structures whether it be two-dimensional or three /dimensional are drawn by connecting certain points. Hence, it can also be stated that shapes are the collection of points.
Lines and line segments
A line is a collection of points that extends up to infinity in two directions or does not have an end. Whereas, a line segment is a part of a line with two endpoints. The portion of a line segment in between these two points and is also represented by them.
**Chord
A chord is a line segment that passes from one point to another point in the circular arc of the circle. It joins the two points of the circle. A chord that connects two points on the circular arc and passes through the center of the circle is termed a diameter.
What is the longest chord of a Circle?
**Answer:
The longest chord of a circle is its diameter, which is double the radius of the circle. The length of the longest chord or diameter is determined by doubling the length of a given radius. Mathematically it can be written as,
**length of longest chord\Diameter = 2r
Where r stands for radius.
Sample Problems
**Question 1: Determine the diameter of a circle with a radius of 8cm.
**Answer:
The given radius (r) of the circle is 8cm.
By the formula,
Diameter = 2r
d = 2 × 8
d = 16cm
**Question 2: Determine the diameter of a circle with a radius of 12cm.
**Answer:
The given radius (r) of the circle is 12cm.
By the formula,
Diameter = 2r
d = 2 × 12
d = 24cm
**Question 3: Determine the diameter of a circle with a radius of 20cm.
**Answer:
The given radius (r) of the circle is 20cm.
By the formula,
Diameter = 2r
d = 2 × 20
d = 40cm
**Question 4: Determine the diameter of a circle with a radius of 16cm.
**Answer:
The given radius (r) of the circle is 16cm.
By the formula,
Diameter = 2r
d = 2 × 16
d = 32cm
**Question 5: Determine the diameter of a circle with a radius of 22cm.
**Answer:
The given radius (r) of the circle is 22cm.
By the formula,
Diameter = 2r
d = 2 × 22
d = 44cm
Unsolved Problems
**Problem 1:
A circle has a radius of 15 cm. Find the diameter of the circle.
**Problem 2:
If the diameter of a circle is 18 cm, determine the radius.
**Problem 3:
A circle has a radius of 5 cm. A chord of length 8 cm is drawn in the circle. Is this chord longer or shorter than the diameter?
**Problem 4:
A chord of a circle is 10 cm long, and the radius of the circle is 6 cm. Does this chord pass through the center of the circle? If yes, find the diameter.
**Problem 5:
Two chords of a circle are equal in length, each measuring 12 cm. The radius of the circle is 10 cm. What is the distance from the center of the circle to each chord?
**Problem 6:
A circle has a diameter of 30 cm. If the radius of another circle is 1.5 times the radius of this circle, find the diameter of the second circle.
**Problem 7:
The radius of a circle is 7 cm. Find the length of the longest chord in this circle.
**Problem 8:
A chord is 6 cm away from the center of the circle, and the radius of the circle is 10 cm. Calculate the length of the chord.