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Parallel Chords

A straight line connecting two points in a circle's circumference or in a curve is called a chord. In a circle, draw two chords. If these two chords are parallel, then they are called as parallel chord. Chord is also called a line segment on the interior part of the circle joining two endpoints lying in the circle.

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Parallel Chord

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The chord is a line segment. The line segment occurs inside the circle. Chord that passes through the center of the circle is generally called as the diameter of the circle. Parallel chord symbol is represented by | |. Following diagram shows the parallel chords.

Parallel chord

The chord AB is parallel to the chord PQ.

Chord point AB | | chord point PQ.

Example Problems on Parallel Chord

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Below are some example problems on parallel chord

Problem 1:

Calculate the length of the chord. The radius of the circle value is 4 cm and angle subtended at the centre by the chord is 45 degree.

Example problems on parallel chord

Solution

The chord length formula is Chord length = 2r sin ($\frac{c}{2}$)

r is the radius of the circle

c is the subtended angle

r value is 4 cm

c value is 45 degree

Chord length = 2*4 sin ($\frac{45}{2}$)

= 8 sin 22.5

= 3.061

The length of the chord value is 3.061

Problem 2:

Calculate the length of the chord. The radius of the circle value is 3 cm and angle subtended at the centre by the chord is 50 degree.

Example problems on parallel chord

Solution

The chord length formula is

Chord length = 2r sin ($\frac{c}{2}$)

r is the radius of the circle

c is the subtended angle

r value is 3 cm

c value is 50 degree

Chord length = 2 * 3 sin ($\frac{50}{2}$)

= 6 sin 25

= 2.53

The length of the chord value is 2.53

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