Library / /31 of 53

, 2005

Geometry Difficulty 3.0 AMC 10/12 Prove it Canada

In the diagram, $\triangle ABC$ is equilateral with side length $4$ . Points $P$ , $Q$ and $R$ are chosen on sides $AB$ , $BC$ and $CA$ , respectively, such that $AP = BQ = CR = 1$ .
(a) Determine the exact area of $\triangle ABC$ . Explain how you got your answer.
(b) Determine the exact areas of $\triangle PBQ$ and $\triangle PQR$ . Explain how you got your answers.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.