14

Part of 2020 BMT Fall

Problems(2)

area of star shaped figure, equal sides, 210^o 2020 BMT Team 14

Source:

In the star shaped figure below, if all side lengths are equal to

3

and the three largest angles of the figure are

210

degrees, its area can be expressed as

\frac{a \sqrt{b}}{c}

a, b

c

are positive integers such that

a

c

are relatively prime and that

b

is square-free. Compute

a + b + c

. https://cdn.artofproblemsolving.com/attachments/a/f/d16a78317b0298d6894c6bd62fbcd1a5894306.png

2020 BMT Individual 14

Source:

B, M

T

be the three roots of the equation

x^3 + 20x^2 -18x-19 = 0

. What is the value of

|(B + 1)(M + 1)(T + 1)|