MathDB

5

Part of 2022 MMATHS

Problems(2)

2022 MMATHS Team Online p5 - min sum of 2 areas, starting with equilateral

Source:

10/1/2023
Equilateral triangle △ABC\vartriangle ABC has side length 66. Points DD and EE lie on BC‾\overline{BC} such that BD=CEBD = CE and BB, DD, EE, CC are collinear in that order. Points FF and GG lie on AB‾\overline{AB} such that FD‾⊥BC‾\overline{FD} \perp \overline{BC}, and GF=GAGF = GA. If the minimum possible value of the sum of the areas of △BFD\vartriangle BFD and △DGE\vartriangle DGE can be expressed as abc\frac{a\sqrt{b}}{c} for positive integers a,b,ca, b, c with gcd(a,c)=1gcd (a, c) = 1 and bb squarefree, find a+b+ca + b + c.
geometryMMATHS
2022 MMATHS Individual p5 - folding a rectange

Source:

10/1/2023
Holding a rectangular sheet of paper ABCDABCD, Prair folds triangle ABDABD over diagonal BDBD, so that the new location of point AA is A′A'. She notices that A′C=13BDA'C =\frac13 BD. If the area of ABCDABCD is 27227\sqrt2, find BDBD.
geometryrectangleMMATHS