the lenth of common chord of two circle which radii 15cmand20cm and which is25cm apart
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first draw the diagram , draw a line connecting the centres of the circles notice that this creates 2 right triangles.
Note also that the common chord divides the line between the centres into two pieces lengths of which we will call x and 25-x.
Call the length of chord 2y.
Using Pythogorean Theorem, x^2+ y^2 = 15^2, and (25-x)^2 + y^2=25^2
Subtract the two equations from each other to get :
(25-x)^2 - x^2 = 25^2 - 15^2
625 -50x + x^2 - x^2 =625 - 225
-50x = -225
x = 225/50 = 9/2.
hope this helps u!!!!!!!!
Note also that the common chord divides the line between the centres into two pieces lengths of which we will call x and 25-x.
Call the length of chord 2y.
Using Pythogorean Theorem, x^2+ y^2 = 15^2, and (25-x)^2 + y^2=25^2
Subtract the two equations from each other to get :
(25-x)^2 - x^2 = 25^2 - 15^2
625 -50x + x^2 - x^2 =625 - 225
-50x = -225
x = 225/50 = 9/2.
hope this helps u!!!!!!!!
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