Orthocentre

Q.

In a right angled triangle, the orthocenter lies on ______________.

1. inside the triangle

2. midpoint of hypotenuse

3. vertex containing the right angle

4. outside the triangle

Q.

The locus of a point equidistant from two intersecting lines is…………

__

Q.

Meaning of CIRCUMCENTRE, CENTROID, INCENTRE, ORTHOCENTRE along with each's FORMULAS ?

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Q.

ABC is an equilateral triangle of side 2a. Find each of its altitudes.

Q. ∆ABC is an equilateral triangle of a side 2a units. Find each of its altitudes.

Q. In an equilateral triangle, the ratio of the sum of the squares of altitudes to the sum of the squares of sides is??

Q. Find the length of altitude AD of an isosceles ∆ABC in which AB = AC = 2a units and BC = a units.

Q. $△ABC$ is an isosceles triangle if the co-ordinates of the base are $B\equiv$ $(1,3)$ and $C\equiv (-2,7)$. Then the coordinates of the vertex $A$ can be

1. $(1,6)$
2. $(-\frac{1}{2},5)$
3. $(\frac{5}{6},6)$
4. $(-7,\frac{1}{9})$

Q. Does a perpendicular line from any vertex in an equilateral triangle be a median on the side it's intersecting?

Q.

The orthocentre of a triangle is the ___________.

1. point of intersection of all the angle bisectors.

2. point of intersection of all the perpendicular bisectors.

3. point of intersection of the medians.

4. point of intersection of all the altitudes from each of the vertices.

Q. Coordinates of the vertices of a triangle $ABC$ are $(12,8),(-2,6)$ and $(6,0)$ then the correct statement is

1. triangle is right and isosceles
2. triangle is isosceles but not right
3. triangle is obtuse
4. the product of the abscissae of the centroid, orthocentre and circumcentre is $160$

Q. The equation of the three sides of a triangle are $x=2,y+1=0$ and $x+2y=4$. The coordinates of the circumcentre of the triangle are

1. $(4,0)$
2. $(2,-1)$
3. $(0,4)$
4. $(-1,2)$

Q. In the given figure, an altitude is drawn to the hypotenuse .The lengths of different segments are marked in the figure. Determine the values of x, y and z in the given case.

Q.

What is the area of a triangle whose vertices are (a , b + c), (a, b - c) and (-a, c)?

1. 2ab

2. 4ac

3. 2ac

4. 4ab

Q. What is the formula to find the vertex of a parabola

Q. How to find the vertex of a parabola