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The circumcentre is outside the triangle - next to the longest line.
The binomial triangle is also known as Pascal's triangle (see Wikipedia link). To generate the triangle, write a pair of 1s in the first line. In the next line write a 1 under and to the left of the 1 in the line above. Then underneath two of the numbers in the line above, write their sum. Finish with a 1 to the right of the 1 in the line above. Keep repeating the last three steps for the next line. If you refer to the line with the pair of 1s as line 1, then the nth line, read across, gives the coefficients for the expansion of the binomial (1+x)n. The last bit explains the name of the triangle.
To work out Pascal's Triangle, you start with two ones at the top. From there on, you add the two numbers above to get the next number. The numbers on the outside will always be 1. ....1.....1 ...1...2...1 ..1..3...3..1 .1.4...6...4.1 1 5 10 10 5 1
The side of the triangle next to the angle is called the adjacent side.
There are 180 degrees in a triangle. Next question?