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in Co-ordinate geometry by (46.6k points)

ABC is a right-angled triangle, right angled at B. The triangle rotates about B such that C and A always lie on two perpendicular lines OX, OY, respectively. The locus of centroid of ΔABC is

(A) A straight line parallel to the perpendicular bisector of OB

(B) A straight line perpendicular to OA

(C) A circle centered at midpoint of OB

(D) None of these 

1 Answer

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by (38.6k points)
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Best answer

Correct option (A) A straight line parallel to the perpendicular bisector of OB

See Fig.

Quadrilateral OCBA is cyclic for which AC is diameter. Therefore, midpoint B′ of CA lies on perpendicular bisector of fixed line segment OB. The centroid G of ΔABC is on BB′ dividing it in the ratio 2:1. Now the locus of B′ is the perpendicular bisector of OB implies that the locus of G is straight line parallel to perpendicular bisector of OB. 

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