If the circumcentre of a triangle lies at the origin and centroid is the middle point of the line joining the points (a2 + 1, a2 + 1) and (2a, –2a), then the orthocenter lies on the line.
(a –1)2 x – (a + 1)2 y = 0
We know from geometry that the circumcentre, centroid and orthocentre of a triangle lie on a line. So the orthocentre of the triangle lies on the line joining the circumcentre (0, 0) and the centroid
Orthocenter of the triangle with vertices (0,0), (3, 4) and (4, 0) is
The number of integral points (integral point means both the coordinates should be integer) that lie exactly in the interior of the triangle with vertices (0, 0), (0, 21), and (21, 0) is
Let P = (–1, 0), Q = (0, 0) and R = be three points. Then the equation of the bisector of the angle PQR is
A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q respectively. Then the point O divides the segment PQ in the ratio.
Let A0, A1 A2 A3 A4 A5 be a regular hexagon described in a circle of unit radius. Then the product of the length of the line segments A0 A1, A0 A2and A0 A4 is
The diagonals of a parallelogram PQRS are long the lines
x + 3y = 4 and 6x – 2y = 7, then PQRS must be a
The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is
The straight lines x + y = 0, 3x + y – 4 = 0, x + 3y – 4 = 0 form a triangle which is
If sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is
If a, b, c are unequal and different from 1 such that the points are collinear, then