HELLO!!! I AM RANDOMPIEKEVIN!!!
Just kidding. I am Kevin.
I started competitive math in the beginning of 8th grade and I took (950) Introduction to Geometry with SamE (Sam Elder) in the beginning of 2015 (still 8th grade). Then, I started (995) Algebra B with jonjoseph (Jon Joseph) in the middle of 2015 with bluespruce and Ridley-C. Then, I started (1020) Intermediate Algebra with djquarfoot (David Quarfoot) in the beginning of 9th grade.
I have improved from a 12 question guy on the AMC 8 to a 19-20 question guy on the AMC 10 in the past year and a half.
Also, I failed the 2016 AMC 10A... o.O
I did decently on the 2016 AMC 10B... 18 correct...
I'm pretty good at writing proofs...
Take a look at this one for 2012 AMC 10B Problem 16:
To determine the area of the figure, you can connect the centers of the circles to form an equilateral triangle with a side of length . We must find the area of this triangle to include the figure formed in between the circles. Since the equilateral triangle has two 30-60-90 triangles inside, we can find the height and the base of each 30-60-90 triangle from the ratios: The height is and the base is . Multiplying the height and base together with , we get . Since there are two 30-60-90 triangles in the equilateral triangle, we multiply the area of the 30-60-90 triangle by :
To find the area of the remaining sectors, which are of the original circles once we remove the triangle, we know that the sectors have a central angle of since the equilateral triangle already covered that area. Since there are pieces gone from the equilateral triangle, we have, in total, of a circle (with radius ) gone. Each circle has an area of , so three circles gives a total area of . Subtracting the half circle, we have:
Summing the areas from the equilateral triangle and the remaining circle sections gives us: .
Yeah pretty good? (The first paragraph was already written by someone else, but I edited it. Also, there was some other stuff that I cleaned up and modified so that it looks as good as it is right now. I'll post some more proofs that I've written below if you want...