Geometry Problem 1324: Quadrilateral, Diagonal, 45 Degrees, Angle Bisector, Isosceles Triangle, Congruence, Machu Picchu, Typography, iPad Apps

Proposition

The figure shows a quadrilateral ABCD with AC = CD and angle ACB = angle ACD = 45 degrees. Points F and E are on CD so that AE is parallel to BC, AB = BE and BE = 2CF. Prove that BD = 2BF = 3BC.
This entry contributed by Sumith Peiris, Moratuwa, Sri Lanka. 

See solution below

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Geometric Art using Mobile Apps

Geometric art is a form of art based on the use and application of geometric figures. A geometric figure is any set or combination of points, lines, surfaces and solids.

A mobile app or mobile application software is a computer program designed to run on smartphones and tablet computers.

Machu Picchu was the ceremonial center of the Incas and is one of the most famous tourist attractions in the world. It is situated between the Andes Mountains and the Amazon jungle in Cusco, Peru.

See also:
Original problem 1324.