formulas and theorems
circle geo
pi(e) trivia
areas
ice skating lore
100
surface area of a sphere?
4*pi*r^2
100
In circle O, chord AC is intersected by OD (D is a point on the circle) at point B. BD=1, AB=3, BC=5. What is the radius of the circle?
8
100
which famous scientist was born on march 14th?
einstein
100
find the area of a regular octagon with side length 1
2+2sqrt2
100
Why is Nathan Chen's "Rocketman" controversial?
the costume is so ugly
200
area of an ellipse knowing semiaxes 'a' and 'b'?
pi*a*b
200
Inside of square ABCD, point E is chosen at random. What is the probability that AEB is an obtuse triangle?
pi/2
200
Some believe that this measurement is better than pi for circle calculations.
Tau (2pi)
200
In triangle ABC, M is the midpoint of BC. Let BC=8 and AM=10. What is the maximum possible area of triangle ABC?
40
200
was Surya Bonaly (the French woman who famously landed a backflip on one leg) the reason why backflips were banned?
no, they were banned for a while because backflips are just dangerous. idk why they unbanned it, its pretty stupid to me.
300
area of a triangle with inradius r and semiperimeter s?
rs
300
(amc) what is the distance between the centers of the incircle and circumcircle of a triangle with side lengths 5,12,13?
sqrt(65)/2
300
which university releases decisions on March 14th? (sometimes 1:59 pm)
MIT
300
what is the area of a triangle with side lengths 2,3,4?
3/4*sqrt15
formula: sqrt[s(s-a)(s-b)(s-c)]
300
the most popular man in figure skating, yuzuru hanyu, was known for the "___ rain" he recieved after each performance. what is it?
pooh rain (stuffed winnie the pooh)
400
in the cyclic quadrilateral above (all vertices lie on the circumference of a single circle), the side lengths and diagonals have what relationship?
AB*CD + DA*BC = AC*BD
ptolemy's
400
(amc) In triangle ABC we have AB=7, AC=8, BC=9. Point D is on the circumscribed circle of the triangle so that AD bisects angle BAC. What is the value of AD/CD?
5/3
400
recite as many digits of pi as you can.
3.14159265358979...
400
C and B lie on circle A (radius 12) and angle CAB=90 degrees. D is the midpoint of AC. DF is perpendicular to AC, with point F on the circle. Another quarter circle CDE is drawn with center D, and E on DF. What is the area of CFE?
15-18sqrt(3)
400
why did alysa need security guards at the 2022 olympics?
chinese spies + her dad apparently escaped the ccp a while ago
500
infinite sum from n=1 of the reciprocal of n^2?
pi^2/6
500
(aime) Point P lies on the diagonal AC of square ABCD with AP>CP. Let O1 and O2 be the circumcenters of triangles ABP and CDP respectively. Given that AB=12 and <O1PO2=120 degrees, then calculate AP [in the form sqrt(a)+sqrt(b)].
2sqrt6+6sqrt2 = sqrt24+sqrt72
500
what is alysa zhang's least favorite type of pie
pumpkin pie (tastes like baby food to me?)
500
square ABCD has side length 2. Arcs AC and BD are centered at B and C, respectively, and intersect at point P. Line segment AC intersects arc BD at point Q. [CQP]?
5/6pi-sqrt3
500
what was kamila valieva's excuse when she was caught doping at the 2022 olympics?
she ate her grandpa's medicine by accident