Library / /61 of 99

, 2023

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

On a square $ABCD$ a line segment $BE$ is drawn such that the point $E$ lies on the side $CD$ . The perimeter of triangle $BCE$ is three-quarters of the perimeter of the square $ABCD$ . The ratio of lengths $CE : CD$ is $\lambda : 1$ . What is the value of $960 \times \lambda$ ?

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: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.