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

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.