What is the radius of the incircle of a triangle?

What is the radius of the incircle of a triangle?

Its radius, the inradius (usually denoted by r) is given by r = K/s, where K is the area of the triangle and s is the semiperimeter (a+b+c)/2 (a, b and c being the sides).

What is called the point of intersection of the angle bisectors of three angles of a triangle?

The point of intersection of angle bisectors of the 3 angles of triangle ABC is the incenter (denoted by I). The incircle (whose center is I) touches each side of the triangle.

What is the inside of a triangle called?

The three angle bisectors intersect in a single point, the incenter, usually denoted by I, the center of the triangle’s incircle. The incircle is the circle which lies inside the triangle and touches all three sides. Its radius is called the inradius.

How do you name an angle bisector?

An angle bisector is a line or ray that divides an angle into two congruent angles . In the figure, the ray →KM bisects the angle ∠JKL . The angles ∠JKM and ∠LKM are congruent.

What does an angle bisector create?

two congruent angles
An angle bisector line divides or makes two congruent angles for any given angle. The same concept applies to a right angle too. A right-angle measures 90°. When an angle bisector is constructed, we get two congruent angles measuring 45° each.

What is the angle bisector of a triangle called?

Ans: A line segment that bisects one of the vertex angles of a triangle and ends up on the corresponding side of a triangle is known as the angle bisector of a triangle. There are three angle bisectors in a triangle. The three angle bisectors of a triangle meet in a single point called the incentre. This point is always inside the triangle.

What is the interior angle bisector theorem in geometry?

The interior angle bisector theorem states that “In a triangle, the interior angle bisector of an angle divides the opposite side to the angle in the ratio of the remaining two sides of a triangle. In the triangle ABC, the angle bisector intersects side BC at point D.

What is the internal and external bisector of a triangle?

Internal and External Bisector of an Angle of Triangle The bisector of a triangle that divides the opposite side internally in the ratio of corresponding sides containing angles is known as the internal bisector of an angle of a triangle.

What is the radius of a circle inscribed in a triangle?

What is the radius of a circle inscribed in a triangle? For any triangle △ABC, let s = 12 (a+b+c). Then the radius r of its inscribed circle is r=Ks=√s (s−a) (s−b) (s−c)s. Recall from geometry how to bisect an angle: use a compass centered at the vertex to draw an arc that intersects the sides of the angle at two points.