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If the join of (x1,y1) and (x2,y2) makes...

If the join of `(x_1,y_1)` and `(x_2,y_2)` makes on obtuse angle at `(x_3,y_3),` then prove that `(x_3-x_1)(x_3-x_2)+(y_3-y_1)(y_3-y_2)<0`

Text Solution

Verified by Experts

The equation of the circle with AB as diameter is
`(x-x_(1))(x-x_(2))+(y-y_(1))(y-y_(2))=0`

Since AB subtends an obtuse angle at `(x_(3),y_(3))` , P lies inside the circle. Therefore,
`(x_(3)-x_(1))(x_(3)-x_(2))+(y_(3)-y_(1))(y_(3)-y_(2))lt0`
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