Solving Circle Chords

Solving circle chords article deals with the defintion and properties of the circle chords and the model problems rerlated to circle chords.

Definition of circle chords:
Circle chord is defined as the line segment that touches the circle at two points. The chord that passes through the center of the circle is known as diameter of the circle. From the diameter of the circle, we can find the radius of the circle.

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Properties to solve the the circle chords:

While solving the chords of the circle, the following properties of the circle need to keep in mind

• When two chords are at equal distance from the center then the two chords are equal in length.
• If two chords are equal in length, then they will at equal distance from the center of circle.
• The line, which is drawn perpendicular to the chord from the center, will bisect the chord.
• The line from the center to the mid point of chord is always perpendicular
• The bisector of chord always passes through the circle center.

Model problems for solving chords:

Problem 1: find the length of the chords of the circle when the two chords intersect each other with in circle.
                                                                                    
Solution:
Since two chords intersect each other in the circle, then
               (CV)(BV) = (AV) (DV)
               7x = 3x(x + 1)
               7x = 3x² + 3x
To solve for x, we will collect like terms and then

we can simplify the equation.
            3x² - 4x = 0
            x (3x - 4) = 0
            x = 0     or    x =4/3
Here x = 0 is an answer, this would make BV = x = 0. We will use x = 4/3.
 no chord will have length of 0.
          CB = CV + BV
         CB = 7 + x
         CB = 7 + (4/3)
         CB = (25/3)

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 2. DV and VN are the two chords of the circle, which are located at the same distance from the center of the circle, when DV is 20cm find the length of the VN chord.

Solution:
If two chords are equal in length, then they will at equal distance from the center of circle.
Since the two chords are located at same distance from the center, so the both chords are of equal length

Length of DV= length of VN
So, the length of the chord, VN is 20cm