Question

If the vertices P, Q, R of a triangle PQR are rational points, which of the following point of the triangle PQR may not be a rational point? 

(1) Centroid 

(2) Incentre 

(3) Circumcentre 

(4) Orthocentre

(A rational point is a point both of whose co-ordinates are rational numbers.)

Answer 1

Correct Option (2) Incentre

Explanation:

(ii) Equations of altitudes will contain only rational coefficient and hence the orthocentre will also be a rational point. 

(iii) Similar argument gives the circumcentre to be a rational point. 

(iv) The length of the sides a, b, c may not be rational and hence the incentre may not be a rational point.