Question

16) The orthocentre of triangle will lie to the exterior of a
a) Equilateral Triangle b) Acute Angled Triangle
c) Obtuse angled triangle d) Right angled triangle​

Answer 1

Step-by-step explanation:

QUESTIONS:-

The orthocentre of triangle will lie to the exterior of a?

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1. The orthocenter is the point where all the three altitudes of the triangle cut or intersect each other. Here, the altitude is the line drawn from the vertex of the triangle and is perpendicular to the opposite side. Since the triangle has three vertices and three sides, therefore there are three altitudes

Orthocenter of a Triangle:-

The orthocenter of a triangle is the point where the perpendicular drawn from the vertices to the opposite sides of the triangle intersect each other.

1. For an acute angle triangle, the orthocenter lies inside the triangle.
2. For the obtuse angle triangle, the orthocenter lies outside the triangle.
3. For a right triangle, the orthocenter lies on the vertex of the right angle.

Take an example of a triangle ABC.

picture in above attachment.

Properties of Orthocenter:-

The orthocenter is the intersection point of the altitudes drawn from the vertices of the triangle to the opposite sides.

1. For an acute triangle, it lies inside the triangle.
2. For an obtuse triangle, it lies outside of the triangle.
3. For a right-angled triangle, it lies on the vertex of the right angle.
4. The product of the parts into which the orthocenter divides an altitude is the equivalent for all 3 perpendiculars.

hope it's helpful ✌️✌️

Answer 2

Step-by-step explanation:

a) Equilateral Triangle