MathDB

2021.C3

Part of Durer Math Competition CD 1st Round - geometry

Problems(1)

two foils overlap on rectangular window 2020-21 Dürer Round1 C3

Source:

12/1/2022
Csenge has a yellow and a red foil on her rectangular window which look beautiful in the morning light. Where the two foils overlap, they look orange. The window is 8080 cm tall, 120120 cm wide and its corners are denoted by A,B,CA, B, C and DD in the figure. The two foils are triangular and both have two of their vertices at the two bottom corners of the window, A and BB. The third vertex of the yellow foil is SS, the trisecting point of side DCDC closer to DD, whereas the third vertex of the red foil is PP, which is one fourth on the way on segment SCSC, closer to CC. The red region (i.e. triangle BPEBPE) is of area 1616 dm2^2. What is the total area of the regions not covered by foil? https://cdn.artofproblemsolving.com/attachments/b/c/ea371aeafde6968506da6f3456e88fa0bddc6d.png
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