MathDB

3

Part of 2019 AIME Problems

Problems(2)

equidistant hexagon

Source: 2019 AIME I #3

3/14/2019
In △PQR\triangle PQR, PR=15PR=15, QR=20QR=20, and PQ=25PQ=25. Points AA and BB lie on PQ‾\overline{PQ}, points CC and DD lie on QR‾\overline{QR}, and points EE and FF lie on PR‾\overline{PR}, with PA=QB=QC=RD=RE=PF=5PA=QB=QC=RD=RE=PF=5. Find the area of hexagon ABCDEFABCDEF.
AMCAIMEAIME Igeometry2019 AIME I2019 AMCarea
Systems of easyuations

Source: 2019 AIME II problem 3

3/22/2019
Find the number of 77-tuples of positive integers (a,b,c,d,e,f,g)(a,b,c,d,e,f,g) that satisfy the following systems of equations: \begin{align*} abc&=70,\\ cde&=71,\\ efg&=72. \end{align*}
AMCAIMEAIME IIalgebrasystem of equations2019 AMC2019 AIME II