The Location of the Orthocentre

Q. Derivation of orthocenter formula of triangle.

Q. In which triangle orthocentre lies outside the triangle?

1. Right angled triangle
2. Obtuse angled triangle
3. Equilateral triangle
4. Acute angled triangle

Q. In which of the following triangles orthocentre lies inside the triangle?

1. Acute angled triangle
2. Right angled triangle
3. Equilateral triangle
4. Obtuse angled triangle

Q. In which triangle orthocentre lies on one of the vertex of the triangle?

1. Obtuse angled triangle
2. Equilateral triangle
3. Obtuse angled triangle
4. Right angled triangle

Q.

Orthocenter always lies inside the triangle.

1. True

2. False

Q. The orthocenter of an acute angled triangle is in the interior of the triangle.

1. True
2. False

Q.

Suppose a triangle is equilateral. Prove that it is equiangular.

Q. The orthocenter of an obtuse angled triangle is in the exterior of the triangle.

1. True
2. False

Q.

For which triangle the orthocenter lies on the triangle and not inside the triangle.

1. Obtuse-angled triangle.

2. Equilateral triangle

3. None of these

4. Acute-angled triangle.

Q.

In a right-angled triangle, one of its angles must be equal to __.

1. 145 deg

2. 180 deg

3. 90 deg

4. 120 deg

Q. The incenter, orthocenter, circumcenter, and centroid lie inside the triangle if it is

1. An obtuse-angled triangle
2. A right-angled triangle
3. An acute-angled triangle
4. None of these

Q. A triangle has three medians.

1. True
2. False

Q. Prove that in a triangle other than an equilateral triangle angle opposite to the longest side is greater than 2/3 of a right angle.

Q. Match the location of the orthocentre of the following triangles with respect to the triangles.

1. 
2. 
3. 
4. Outside
5. Inside
6. On the triangle

Q. In which triangle orthocentre lies on one of the vertex of the triangle?

1. Equilateral triangle
2. Obtuse angled triangle
3. Obtuse angled triangle
4. Right angled triangle

Q. In an obtuse angled triangle, the orthocentre lies outside the triangle.

1. True
2. False

Q. In an acute angled triangle, the orthocentre lies outside the triangle.

1. True
2. False

Q. In a right angled triangle, the orthocentre lies at the vertex containing the right angle.

1. True
2. False