MathDB

10

Part of 2017 AIME Problems

Problems(2)

Wot n' Imagination

Source: 2017 AIME I #10

3/8/2017
Let z1=18+83iz_1 = 18 + 83i, z2=18+39i,z_2 = 18 + 39i, and z3=78+99i,z_3 = 78 + 99i, where i=−1i = \sqrt{-1}. Let zz be the unique complex number with the properties that z3−z1z2−z1⋅z−z2z−z3\frac{z_3 - z_1}{z_2 - z_1} \cdot \frac{z - z_2}{z - z_3} is a real number and the imaginary part of zz is the greatest possible. Find the real part of zz.
2017 AIME 1 problem 10Wot n
Jane Eyrectangle

Source: 2017 AIME II #10

3/23/2017
Rectangle ABCDABCD has side lengths AB=84AB=84 and AD=42AD=42. Point MM is the midpoint of AD‾\overline{AD}, point NN is the trisection point of AB‾\overline{AB} closer to AA, and point OO is the intersection of CM‾\overline{CM} and DN‾\overline{DN}. Point PP lies on the quadrilateral BCONBCON, and BP‾\overline{BP} bisects the area of BCONBCON. Find the area of △CDP\triangle{CDP}.
AIMEAIME IAIME II