MathDB

3

Part of 2017 May Olympiad

Problems(2)

Good question

Source: May Olympiad(Olimpiada de Mayo) 2017

10/2/2017
Let ABCDABCD be a quadrilateral such that ∠ABC=∠ADC=90º\angle ABC = \angle ADC = 90º and ∠BCD\angle BCD > 90º90º. Let PP be a point inside of the ABCDABCD such that BCDPBCDP is parallelogram, the line APAP intersects BCBC in MM. If BM=2,MC=5,CD=3BM = 2, MC = 5, CD = 3. Find the length of AMAM.
geometryparallelogram
computational geometry for 13yo, areas of rhombuses

Source: May Olympiad (Olimpiada de Mayo) 2017 L1

9/10/2018
Let ABCDABCD be a rhombus of sides AB=BC=CD=DA=13AB = BC = CD= DA = 13. On the side ABAB construct the rhombus BAFEBAFE outside ABCDABCD and such that the side AFAF is parallel to the diagonal BDBD of ABCDABCD. If the area of BAFEBAFE is equal to 6565, calculate the area of ABCDABCD.
geometryrhombusareas