Skip to content

Incircle Explorer

Run Fullscreen

About This MicroSim

This interactive visualization demonstrates the incenter of a triangle - the intersection point of the three angle bisectors. The incenter is the center of the inscribed circle (incircle) that touches all three sides.

Key Concepts

Angle Bisectors

An angle bisector divides an angle into two equal parts. Every triangle has three angle bisectors, one from each vertex.

The Incenter (I)

  • The incenter is always inside the triangle (for any triangle type)
  • It is equidistant from all three sides
  • It is the center of the incircle (the largest circle that fits inside)

Inradius Formula

The radius of the incircle can be calculated as:

\[r = \frac{\text{Area}}{s}\]

where \(s\) is the semi-perimeter: \(s = \frac{a + b + c}{2}\)

Interactions

  • Drag vertices A, B, or C to reshape the triangle
  • Watch how the incircle always touches all three sides
  • Observe the tangent points where the incircle meets each side

Learning Objectives

  • Understand that angle bisectors meet at a single point
  • Identify the incenter as equidistant from all sides
  • Recognize that the incircle touches all three sides
  • Apply the inradius formula: r = Area / s

Bloom's Taxonomy Level

Understanding and Applying