MathDB

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Part of 2004 Oral Moscow Geometry Olympiad

Problems(2)

half triangle area wanted, midpoints in convex quadrilateral

Source: 2004 Oral Moscow Geometry Olympiad grade 9 p1

10/27/2020
In a convex quadrilateral ABCDABCD, EE is the midpoint of CDCD, FF is midpoint of ADAD, KK is the intersection point of ACAC with BEBE. Prove that the area of triangle BKFBKF is half the area of triangle ABCABC.
areasgeometry
line connecting midpoints BE,AD divide diagonals AC,BC in the same ratio

Source: 2004 Oral Moscow Geometry Olympiad grade 10 p1

10/28/2020
EE and FF are the midpoints of the sides BCBC and ADAD of the convex quadrilateral ABCDABCD. Prove that the segment EFEF divides the diagonals ACAC and BDBD in the same ratio.
geometryratiomidpoints