# Relationships Between Six Incircles

## TL;DR

This paper investigates the relationships between the radii of incircles of six smaller triangles formed inside a larger triangle by cevians passing through an interior point P.

## Contribution

It presents new theorems describing how the incircle radii of these six subtriangles relate to each other based on the position of P.

## Key findings

- Derived formulas linking the incircle radii of the six smaller triangles.
- Established conditions for equal incircle radii among the six triangles.
- Provided geometric insights into cevian configurations and incircle relationships.

## Abstract

If P is a point inside triangle ABC, then the cevians through P divide triangle ABC into six smaller triangles. We give theorems about the relationship between the radii of the circles inscribed in these triangles.