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If the vertices of a triangle PQR are ra...

If the vertices of a triangle `PQR` are rational points, then which of the following points of this triangle may not be rational -
(a)   Centroid     (b)   Incenter
(c)    Circumcenter     (d)    Orthocenter

Text Solution

Verified by Experts

G is rational
I may not be rational
`x^2+y^2+2gx+2fy+c=0`
g and f are rational, circumcenter of ration.
`(y-y_2)/(x-x_2)=(y_3-y_2)/(x_3-x_2)-(1)`
`(y-y_1)/(x-x_1)=(y_3-y_2)/(x_3-x_2)-(2)`
From 1 and 2
orthocenter is a rational.
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