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BodhiAI
Nov. 15, 2019

Equation of Chords of Contact & General Chord:

Length of Common Chord

Let

and

be the two equations of the circles having centres and and radii r1 and r2 respectively.

Let p1 be the perpendicular distance from the centre C1 to that of the common chord.

Now, from the figure, we have

or

or

Problem Solving Trick

To find the length of common chord, follow the following step method.

Step I As a usual practice, first of all make the coefficients of x2 and y2 unity in both the equations.

Now, find the centre(s) C1 and C2 of both the circles and the radii r1 and r2

Step II Find the equation of common chord, such that

Step III Calculate the perpendicular distance p1 or p2 from centre to that of common chord.

Step IV Find the length of common chord by using the relation

Length of Common Chord