One Point per Side
Triangle ABC has area 1. Points P, Q, R are chosen independently and uniformly at random on sides BC, CA and AB respectively (uniform with respect to length). What is the expected area of triangle PQR? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- Monochromatic Triangles 2.0/10
- Like Next to Like 2.0/10
- Expected Disorder 2.0/10
Source: Classic geometric-probability exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.