Law of cosines . The power of the point with respect to the circle is equal to both and . Therefore, which is the law of cosines. Using algebraic measures for line segments (allowing negative numbers as lengths of segments) the case of obtuse angle () and acute angle () can be treated simultaneously. By using the law of sines and knowing that the angles of a triangle must sum to 180 degrees, we have the following system of equations (the three unknowns are the angles): Then, by using the third equation of the system, we obtain a system of two equations in
Bernoulli's triangle component in row "n" and column "k", then: As in Pascal's triangle and other similarly constructed triangles, sums of components along diagonal paths in Bernoulli's triangle result in the Fibonacci numbers. Bernoulli's triangle Bernoulli's triangle is an array of partial sums of the binomial coefficients. For any non-negative integer "n" and for any integer "k" included between 0 and "n", the component in row "n" and column "k" is given by: i.e., the sum of the first "k" "n"th-order binomial coefficients. The first rows of Bernoulli's triangle are: Similarly to Pascal's triangle, each component of Bernoulli's triangle is the sum