MathDB

A2/B4

Part of 2020 Princeton University Math Competition

Problems(3)

2020 PUMaC Algebra A2 / B4

Source:

1/1/2022
Let CC denote the curve y2=x(x+1)(2x+1)6y^2 =\frac{x(x+1)(2x+1)}{6}. The points (1/2,a)(1/2, a),(b,c)(b, c), and (24,d)(24, d) lie on CC and are collinear, and ad<0ad < 0. Given that b,cb, c are rational numbers, find 100b2+c2100b^2 + c^2.
algebra
2020 PUMaC Geometry A2 / B4

Source:

12/31/2021
Hexagon ABCDEFABCDEF has an inscribed circle Ω\Omega that is tangent to each of its sides. If AB=12AB = 12, ∠FAB=120o\angle FAB = 120^o, and ∠ABC=150o\angle ABC = 150^o, and if the radius of Ω\Omega can be written as m+nm +\sqrt{n} for positive integers m,nm, n, find m+nm + n.
geometry
2020 PUMaC NT A2 / B4

Source:

1/1/2022
How many ordered triples of nonzero integers (a,b,c)(a, b, c) satisfy 2abc=a+b+c+42abc = a + b + c + 4?
number theory