What is Exradii of a triangle?
The circle with centre I₁ and touching the three sides of the triangle is called excircle of triangle ABC opposite to the vertex A. The radius of this ex-circle is called ex-radius of triangle ABC and it is denoted by r₁. The excentres of ΔABC opposite to the vertices B, C are respectively denoted by I₂, I₃.
How do you make a excircle?
In order to construct the excircles, we must first extend all the sides of the triangles. Next, we have to bisect the exterior angles that are between the two extended sides to which the triangle will be tangent. The intersection of the angle bisectors is the center of that excircle.
What is ex radii of a circle?
An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three distinct excircles, each tangent to one of the triangle’s sides.
What is ex-radius of equilateral triangle?
For an equilateral triangle, all 3 ex radii will be equal. Area = r1 * (s-a), where ‘s’ is the semi perimeter and ‘a’ is the side of the equilateral triangle. ∴ ex-radius of the equilateral triangle, r1 = As−a = √3a2.
How do you find the Exradii of a triangle?
The exradii of a triangle with sides a, b, c are given by ra = ∆ s – a , rb = ∆ s – b , rc = ∆ s – c . (a + b + c). r ra =s – a s .
How do you find the Excentre?
A point where the bisector of one interior angle and bisectors of two external angle bisectors of the opposite side of the triangle, intersect is called the excenter of the triangle. There are in all three excentres of a triangle. a,b,c are the lengths of sides BC, AC and AB respectively.
What is the excircle?
An excircle is a circle tangent to the extensions of two sides of a triangle and the third side.
What is incircle and circumcircle?
An incircle is a circle drawn inside the polygon that touches all sides of the polygon. The circumcircle is a circle that passes through all the vertices of a triangle (polygon).