Incircle of a triangle

The incircle of a triangle is the largest circle that fits perfectly inside it, touching all three sides. Its center, called the incenter, is the point where the angle bisectors (lines dividing each angle into two equal parts) meet. The radius of this circle, called the inradius, is the distance from the incenter to any side of the triangle. The incircle helps in understanding properties like symmetry and evenly distributing space within the triangle, and it has applications in construction, design, and geometric proofs.