MathDB

2

Part of 2003 May Olympiad

Problems(2)

calculations in a rectangle

Source: May Olympiad (Olimpiada de Mayo) 2003 L2

9/15/2018
Let ABCDABCD be a rectangle of sides AB=4AB = 4 and BC=3BC = 3. The perpendicular on the diagonal BDBD drawn from AA cuts BDBD at point HH. We call MM the midpoint of BHBH and NN the midpoint of CDCD. Calculate the measure of the segment MNMN.
geometryrectangleperpendicular
area of a triangle, right triangle related (May Olympiad 2003 L1)

Source:

5/11/2019
The triangle ABCABC is right in AA and RR is the midpoint of the hypotenuse BCBC . On the major leg ABAB the point PP is marked such that CP=BPCP = BP and on the segment BPBP the point QQ is marked such that the triangle PQRPQR is equilateral. If the area of triangle ABCABC is 2727, calculate the area of triangle PQRPQR .
geometryarea of a triangleareasright triangle