Orthocentre

Q. In triangle centroid, circumcentre, incentre and orthocentre are all the same point.

1. a scalene
2. an equilateral
3. an isosceles
4. a right-angled

Q. The orthocenter of the triangle formed by the lines $xy=0$ and $x+y=1$ is

1. $(\frac{1}{2},\frac{1}{2})$
2. $(\frac{1}{3},\frac{1}{3})$
3. $(0,0)$
4. $(\frac{1}{4},\frac{1}{4})$

Q.

If Q is the foot of the perpendicular of the point P(3, 6) on the line x - 2y + 4 = 0, then the equation of PQ is

1. 2x + y = 12

2. x + 2y = 12

3. x + 2y + 12 = 0

4. 2x + y + 12 = 0

Q. The points $A(0,0),B(\cos \alpha ,\sin \alpha )$, and $C(\cos \beta ,\sin \beta )$ are the vertices of a right-angled triangle if

1. ${\sin }^2\frac{\alpha -\beta }{2}=\frac{1}{2\sqrt{2}}$
2. $\cos \frac{\alpha -\beta }{2}=-\frac{1}{\sqrt{2}}$
3. ${\cos }^2\frac{\alpha -\beta }{2}=\frac{1}{2\sqrt{2}}$
4. $\sin \frac{\alpha -\beta }{2}=-\frac{1}{\sqrt{2}}$

Q. The locus of the orthocentre of the triangle formed by the lines $(1+p)x-py+p(1+p)=0$,
$(1+q)x-qy+q(1+q)=0$ and $y=0$ where $p\ne q$, is

1. A hyperbola
2. A parabola
3. An ellipse
4. A straight line

Q.

Let k be an integer such that the triangle with vertices (k, -3k), (5, k) and (-k, 2) has area 28 sq units. Then, the orthocentre of this triangle is at the point

1. $(2,-\frac{1}{2})$
2. $(1,\frac{3}{4})$
3. $(1,-\frac{3}{4})$
4. $(2,\frac{1}{2})$

Q. The co-ordinates of the circumcentre of triangle if $P\equiv (2,7),Q\equiv (-5,8),R\equiv (-6,1)$ are the vertices of triangle is (-2, 4)
If true then enter $1$ and if false then enter $0$

Q. X and Y are points on the side LN of the triangle LMN such that LX=XY=YN.Through X, a line is drawn parallel to LM to meet MN at Z. Prove that ar(LZY)=ar(MZYX).

Q.

The point of intersection of the three medians of a triangle is called its _______

1. Centroid

2. Orthocentre

3. Incentre

4. Circumcentre

Q. Find the third vertex of an equilateral triangle whose other two vertices are (1, 1) and (-1, -1) respectively is 3

1. $\left(\sqrt{3},-\sqrt{3}\right)$
2. $\left(-\sqrt{3},\sqrt{3}\right)$
3. $\left(-\sqrt{3},-\sqrt{3}\right)$
4. Both 1 and 2

Q.

Equations to the sides of a triangle are $x-3y=0$, $4x+3y=5$ and $3x+y=0$. The line $3x-4y=0$ passes through the

1. incentre

2. circumcentre

3. centroid

4. orthocentre of the triangle