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SAT Math Practice Question #26647 - SATify | SATify

#26647

combinatorics

geometry

probability

Relative Motion

hard

150 sec

Three distinct segments are chosen at random among the segments whose end-points are the vertices of a regular $8$ -gon. What is the probability that the lengths of these three segments are the three side lengths of a triangle with positive area?

A.

$\frac{35}{39}$

B.

$\frac{34}{39}$

C.

$\frac{36}{39}$

D.

$\frac{4}{39}$

E.

$\frac{33}{39}$