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UKMT Mathematical Olympiad for Girls, 2020

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

Twelve points, four of which are vertices, lie on the perimeter of a square. The distance between adjacent points is one unit. Some of the points have been connected by straight lines. BB is the intersection of two of those lines, as shown in the diagram.

(a) Find the ratio AB:BCAB : BC. Give your answer in its simplest form.

(b) Find the area of the shaded region.

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