MathDB

5

Part of 1987 Mexico National Olympiad

Problems(1)

for no point M 2 triangles and a rectangle have the same area

Source: 1st Mexican Mathematical Olympiad 1987 OMM P5

7/27/2018
In a right triangle ABCABC, M is a point on the hypotenuse BCBC and PP and QQ the projections of MM on ABAB and ACAC respectively. Prove that for no such point MM do the triangles BPM,MQCBPM, MQC and the rectangle AQMPAQMP have the same area.
geometryrectangleareasright triangle