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The Incentre Of The Triangle With Vertices 1 Sqrt3 0 0 And 2 0 Is

1) (1,√3/2) 2) (2/3, 1/√3) 3) (2/3, √3/2) 4) (1, 1/√3) Solution: Option (4) (1, 1/√3) Let the vertices of triangle ABC be A (1, √3),... View Article

If The Centroid Of The Triangle Formed By The Points 0 0 Cos Theta Sin Theta And Sin Theta Cos Theta Lies On The Line Y 2x Then Theta Is Equal To

1) tan-1 2 2) tan-1 3 3) tan-1 (-3) 4) tan-1 (-2) Solution: Option (3) tan-1 (-3) Given that the vertices of a triangle are O(0, 0),... View Article

If Orthocentre And Circumcentre Of A Triangle Are Respectively 1 1 And 3 2 Then The Coordinates Of Its Centroid Are

1) (7/3, 5/3) 2) (5/3, 7/3) 3) (7, 5) 4) None of these Solution: Option (1) (7/3, 5/3) As we know that the centroid of the triangle... View Article

In Abc G Is The Centroid D Is The Midpoint Of Bc If A 23 And G 75 Then The Point D Is

1) (9/2, 4) 2) (19/2, 6) 3) (11/2, 11/2) 4) (8, 13/2) Solution: Option (2) (19/2, 6) Given that G is the centroid of a triangle ABC.... View Article

If A Vertex Of A Triangle Is 1 1 And The Midpoints Of Two Sides Through The Vertex Are 1 2 And 3 2 Then The Centroid Of The Triangle Is

1) (1, 7/3) 2) (1/3, 7/3) 3) (-(1/3), 7/3) 4) (-1, 7/3) Solution: Option (1) (1, 7/3) Given that, the vertex of a triangle is (1, 1)... View Article

If O 0 0 P 34 Q 60 Be The Vertices Of The Opqthe Point R Inside Opq Is Such That The Triangles Opr Pqr And Oqr Are Of Equal Area

1) (4/3, 3) 2) (3, 2/3) 3) (3, 4/3) 4) (4/3, 2/3) Solution: Option (3) (3, 4/3) Let the coordinates of R be (a, b) Given that the... View Article

The Circumcentre Of A Triangle Formed By The Lines Xy 2x 2y 4 0 And X Y 2 0 Is

1) (-1, -1) 2) (0, -1) 3) (1, 1) 4) (-1, 0) Solution: Option (1) (-1, -1) Given equations are xy+ 2x+ 2y+ 4 = 0 (or) (x+2) (y+2)... View Article

The Vertices P Q And R Of A Triangle Are 2 1 5 2 And 3 4 Respectively Then The Circumcentre Is

1) (13/4, -9/4) 2) (- (13/4), 9/4) 3) (-(13/4), -(9/4)) 4) (13/4, 9/4) Solution: Option (4) (13/4, 9/4) Given that, P(2, 1), Q(5, 2)... View Article

The Coordinates Of The Orthocentre Of The Triangle Formed By 0 0 8 0 And 4 6 Is

1) (4, 0) 2) (6, 3) 3) (6, 0) 4) None of these Solution: Option (4) None of these Let ABC be a triangle and their vertices are A(0,... View Article

Circumcentre Of The Triangle Whose Vertices Are 0 0 3 0 And 0 4 Is

1) (3/2, 2) 2) (2, 3/2) 3) (0, 0) 4) None of these Solution: Option (1) (3/2, 2) Let A(0, 0), B(3, 0) and C(0, 4) be the vertex and... View Article

The Circumcentre Of The Triangle Formed By The Lines Y X Y 2x And Y 3x 4 Is

1) (6, 8) 2) (6, - 8) 3) (3, 4) 4) (-3, - 4) Solution: Option (2) (6, -8) X2 + y2 = (x+4)2 + (y+8)2 8x+16y+80 = 0 …(1) X2+y2 =... View Article

The Circumcentre Of The Triangle With Vertices 0 30 4 0 And 30 0 Is

1) (10, 10) 2) (10, 12) 3) (12, 12) 4) (15, 15) 5) (17, 17) Solution: Option (5) (17, 17) Assume that the circumcentre of a... View Article

The Centroid If The Abc Where A 2 3 B 8 10 And C 5 5 Is

1) (5, 6) 2) (6, 5) 3) (6, 6) 4) (15, 18) Solution: Option (1) (5, 6) The centroid of a triangle ABC = ((2+8+5)/3, (3+10+5)/3) =... View Article

The Coordinates Of The Incentre Of The Triangle Having Sides 3x 4y 0 5x 12y 0 And Y 15 0 Are

1) (-1, 8) 2) (1, - 8) 3) (2, 6) 4) None of these Solution: Option (1) (-1, 8) Given equations: 3x - 4y = 0 …(1) 5x+12y = 0 …(2)... View Article

The Vertices Of A Triangle Are 6 0 0 6 And 6 6 The Distance Between Its Circumcentre And Centroid Is

1) 2 2) √2 3) 1 4) 2√2 Solution: Option (2) √2 Given that the vertices (6, 0), (0, 6) and (6, 6) form a right angled triangle. The... View Article

Three Distinct Points A B And C Given In The Twodimensional Coordinate Plane Such That The Ratio Of The Distance Of Any One Of Them From

1) (5/4, 0) 2) (5/2, 0) 3) (5/3, 0) 4) (0, 0) Solution: Option (1) (5/4, 0) Let assume that P be a general point (x, y), such that... View Article