The coordinates of two points `Pa n dQ` are `(x_1,y_1)a n d(x_2,y_2)a n dO` is the origin. If the circles are described on `O Pa n dO Q` as diameters, then the length of their common chord is (a)`(|x_1y_2+x_2y_1|)/(P Q)` (b) `(|x_1y_2-x_2y_1|)/(P Q)` `(|x_1x_2+y_1y_2|)/(P Q)` (d) `(|x_1x_2-y_1y_2|)/(P Q)`

Options

A. `(|x_(1)y_(2)+x_(2)y_(1)|)/(PQ)`
B. `(|x_(1)y_(2)-x_(2)y_(1)|)/(PQ)`
C. `(|x_(1)x_(2)-y_(2)y_(1)|)/(PQ)`
D. `(|x_(1)x_(2)+y_(2)y_(1)|)/(PQ)`

Answer

2

Explanation

`OR =(2xx "area of "Delta OPQ)/(PQ)`
`=(2xx|(1)/(2)(x_(1)y_(2)-x_(2)y_(1))|)/(PQ)=(|x_(1)y_(2)-x_(2)y_(1)|)/(PQ)`