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# Principal Properties of Right Triangles

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## Inradius and Circumradius of Right Triangle

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Circular geometry contains different kind of radius like inradius and circumradius. Inradius is a radius, which is the part of incircle or insphere and circumradius is a radius, which is part of circumcircle or cicumsphere.

We use the following steps for evaluating an inradius and circumradius:
Step 1: First, we have to check what kind of polygon we have, like regular polygon or irregular polygon.
Step 2: If we have regular polygon, then we use following formula for evaluation of inradius and circumradius:

Inradius of regular polygon = $\frac{1}{2}$$\times a \times \cot$$\frac{\pi}{n}$,

Here, a is side length and n is number of side of polygon.
Circumradius of regular formula = $\frac{1}{2}$$\times a \times \csc$$\frac{\pi}{n}$

Here, ‘a’ is the side length and n is the number of sides of polygon.

Step 3: If we have irregular polygon, then we should calculate inradius and circumradius of polygon manually by their graphic structure.

## Altitude of Right Triangle

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Dropping of a geometry altitude is a special case of orthogonal projection. An altitude in geometry is the shortest distance from the top or vertex of a geometric figure to the opposite side or base of that geometric figure.

Geometry altitude of a triangle is nothing but a straight line through the top point or vertex and it makes a right angle or is perpendicular with a line opposite of the triangle or base. The line which contains the opposite side of any geometric figure is called the extended base of the geometry altitude. The point where the intersection takes place between the extended base and the altitude in geometry is called the foot of the altitude. The distance between the base and the vertex of any geometric figure is called the length of the altitude or simply altitude in geometry. We can draw an altitude in geometry from the vertex to the foot of a geometric figure by a process known as dropping.

Three geometry altitude of a triangle intersect at a single point called an orthocenter.

Geometry altitude can be used to calculate the area of a triangle by using the formula $\frac{1}{2}$ bh, where b is the length of the base and h is the length of the altitude or height of the triangle. The altitudes of a triangle are related to the sides of the triangle through many theorems like equilateral triangle theorem, inradius theorems, area theorem and so on. There is one very important formula called Heron’s formula which relates to the sides and altitude of a triangle.

In an isosceles triangle, the foot of the geometry altitude is the midpoint of the base of the triangle. And, the altitude will form the angle bisector of the vertex of the triangle.