3

Part of 2012 May Olympiad

Problems(2)

May Olympiad 2012, Level 2, Problem 3

Source:

ABC

be a triangle such that

\angle{ABC} = 2\angle{BCA}

\angle{CAB}>90^\circ

M

be the midpoint of

BC

. The line perpendicular to

AC

that passes through

C

AB

D

\angle{AMB} = \angle{DMC}

geometryperpendicular bisectorangle bisector

paper folding for half area of ABCD (May Olympiad 2012 L1)

Source:

From a paper quadrilateral like the one in the figure, you have to cut out a new quadrilateral whose area is equal to half the area of the original quadrilateral.You can only bend one or more times and cut by some of the lines of the folds. Describe the folds and cuts and justify that the area is half. https://2.bp.blogspot.com/-btvafZuTvlk/XNY8nba0BmI/AAAAAAAAKLo/nm4c21A1hAIK3PKleEwt6F9cd6zv4XffwCK4BGAYYCw/s400/may%2B2012%2Bl1.png

geometryareapaper