Question

From 5 points (4 vertices of a square + 1 intersection point of diagonals), how many triangles can be formed?

• A. 4
• B. 6
• C. 8
• D. 10

Hint:

Subtract collinear triplets from total combinations \( \binom{n}{3} \) to count valid triangles.

Answer 1

The Correct Option is C

Total number of triangles from 5 points: \[ \binom{5}{3} = 10 \] But check: Are all triangles valid? Yes, except when 3 points are collinear. In a square with diagonals intersecting, the center (intersection) and endpoints of a diagonal are collinear. So, the center and the two opposite corners lie on a straight line — forming 1 invalid triangle. \[ \text{Valid triangles} = 10 - 2 = \boxed{8} \]