BodhiAI

Nov. 15, 2019
**Length of Common Chord**

**Let **

**and **

**be the two equations of the circles having centres and and radii r _{1 }and r_{2} respectively.**

**Let p _{1 }be the perpendicular distance from the centre C_{1} 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 x^{2 }and y^{2 }unity in both the equations.

Now, find the centre(s) C_{1 }and C_{2} of both the circles and the radii r_{1} and r_{2}

Step II Find the equation of common chord, such that

Step III Calculate the perpendicular distance p_{1 }or p_{2} from centre to that of common chord.

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

Length of Common Chord