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UKMT Senior Kangaroo, 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 $960 \times \lambda$ ?

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