MathDB

3

Part of 2022 AIME Problems

Problems(2)

wait if this is english why do i have to translate it???

Source: 2022 AIME I #3

2/9/2022
In isosceles trapezoid ABCDABCD, parallel bases AB‾\overline{AB} and CD‾\overline{CD} have lengths 500500 and 650650, respectively, and AD=BC=333AD=BC=333. The angle bisectors of ∠A\angle{A} and ∠D\angle{D} meet at PP, and the angle bisectors of ∠B\angle{B} and ∠C\angle{C} meet at QQ. Find PQPQ.
AMCAIMEAIME I
3D Geo? At #3?

Source: 2022 AIME II Problem 3

2/17/2022
A right square pyramid with volume 5454 has a base with side length 6.6. The five vertices of the pyramid all lie on a sphere with radius mn\frac mn, where mm and nn are relatively prime positive integers. Find m+nm+n.
AMCAIMEAIME II