MathDB

15

Part of 2015 ASDAN Math Tournament

Problems(2)

2015 Guts #15

Source:

7/28/2022
Let ABCDABCD be a regular tetrahedron of side length 1212. Select points E,F,G,HE,F,G,H on AC,BC,BD,ADAC,BC,BD,AD, respectively, such that AE=BF=BG=AH=3AE=BF=BG=AH=3. Compute the area of quadrilateral EFGHEFGH.
2015Guts Test
2015 Team #15

Source:

8/3/2022
In a given acute triangle △ABC\triangle ABC with the values of angles given (known as aa, bb, and cc), the inscribed circle has points of tangency D,E,FD,E,F where DD is on BCBC, EE is on ABAB, and FF is on ACAC. Circle γ\gamma has diameter BCBC, and intersects EF‾\overline{EF} at points XX and YY. Find XYBC\tfrac{XY}{BC} in terms of the angles aa, bb, and cc.
2015team test