Solved Probelms on Chord of a Circle
Problem 1: A circle is an angle of 70 degrees whose radius is 5cm. Calculate the chord length of the circle.
Solution:
Given
- Radius = 5 cm
- Angle = 70°
Now,
chord length = 2R × Sin [angle/2]
= 2 × 5 × sin [70/2]
= 10 × sin35°
= 10 × 0.5736
= 5.73cm
Problem 2: In a circle, the radius is 7cm and the perpendicular distance from the centre of the circle to its chords is 6cm. Calculate the length of the chord.
Solution:
Given
- Radius = 7 cm
- Distance = 6 cm
Now,
Length of the chord = 2 √r2 – d2
= 2 √72 – 62
= 2 √ 49- 36
= 2 √13cm
Problem 3: A circle is an angle of 60 degrees whose radius is 12cm. Calculate the chord length of the circle.
Solution:
Given
- Radius = 12 cm
- Angle = 60°
Now,
chord length = 2R × Sin [angle/2]
⇒ 2 × 12 × sin [60/2]
⇒ 24 × sin30°
⇒ 24 × 0.5
⇒ 12cm
Problem 4: In a circle, the radius is 16cm and the perpendicular distance from the centre of the circle to its chords is 5cm. Calculate the length of the chord.
Solution:
Given
- Radius = 16 cm
- Distance = 5 cm
Now,
Length of Chord = 2 √r2– d2
⇒ 2 √(16)2 – (5)2
⇒ 2 √ 256- 25
⇒ 2 √231
⇒ 2 × 15.1
⇒ 30.2cm
Problem 6: Calculate the length of a common chord between the circles of radius 6cm and 5cm respectively. And, the distance between the two centres was measured to be 8cm.
Solution:
Given
Distance between the two centers = 8cm
Radius of the two circles is R1 and R2 with lengths 6cm and 5cm respectively
Now,
Length of a common chord of two circles = (2R1 × R2) / Distance between two centers of circles
⇒ 2 × 5 × 6/8
⇒ 60/8
⇒ 7.5 cm
Chords of a Circle
Chord of a circle is the line that joints any two points on the circumference of the circle. A circle can have various chords and the largest chord of a circle is the diameter of the circle. We can easily calculate the length of the chord using the Chord Length Formula. As the name suggests it is the formula for calculating the length of the chord in a circle in Geometry.
In this article, we will learn about the definition of the chord, theorems of the chords and the circle, explain its properties, and the formulas to calculate the length of the chord using different methods. The article also has some solved sample problems for better understanding.
Table of Content
- Circle Definition
- Chord of a Circle Definition
- What is Chord Length Formula?
- Chord of a Circle Theorems
- Properties of Chords of a Circle
- Solved Probelms
- FAQs
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