Solution. A total of 35 lines are constructed (10 defined by the points $A_{i}$, ten defined by the points $B_{i}$, and another 15 lines connecting the points $B_{i}$ to the vertices of the pentagon). Each of the points $A_{i}$ contains exactly 7 of these lines, and each of the points $B_{i}$ contains exactly 8 of these lines. The number of points in which exactly two of the constructed lines intersect is equal to

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3. Given a convex pentagon $A_{1} A_{2} A_{3} A_{4} A_{5}$ and points $B_{1}, B_{2}, B_{3}, B_{4}, B_{5}$, such that each side of the pentagon contains exactly one of these points. All lines defined by the vertices of the pentagon and the points $B_{1}, B_{2}, B_{3}, B_{4}$, $B_{5}$ are constructed. If it is known that (excluding the points $A_{i}$ and $B_{j}$) no three of these lines intersect at a single point and no two are parallel, determine the number of all points where exactly two of these lines intersect.