MathDB

2

Part of 2019 BMT Spring

Problems(5)

Know thine reflections - analytic geometry

Source: BMT 2019 Spring Algebra 2

10/8/2021
Find the point p p in the first quadrant on the line y=2x y = 2x such that the distance between p p and p′ p' , the point reflected across the line y=x y = x , is equal to 32 \sqrt{32} .
geometryanalytic geometry
I went into this test full of confidence...and got wrecked (BMT 2019 Geo #2)

Source:

5/9/2019
A set of points in the plane is called full if every triple of points in the set are the vertices of a non-obtuse triangle. What is the largest size of a full set?
Otherwise known as the much easier coin problem (BMT 2019 Discrete #2)

Source:

5/22/2019
Sylvia has a bag of 10 coins. Nine are fair coins, but the tenth has tails on both sides. Sylvia draws a coin at random from the bag and flips it without looking. If the coin comes up tails, what is the probability that the coin she drew was the 2-tailed coin?
angle wanted, midpoint, 2 circles 2019 BMT Individual 2

Source:

1/5/2022
Let A,B,CA, B, C be unique collinear pointsAB=BC=13 AB = BC =\frac13. Let PP be a point that lies on the circle centered at BB with radius 13\frac13 and the circle centered at CC with radius 13\frac13 . Find the measure of angle ∠PAC\angle PAC in degrees.
geometryanglesmidpoint
2019 BMT Team 2

Source:

1/7/2022
Find the remainder when 220192^{2019} is divided by 77.
number theory