GATE CS 2021 Set 1 — Question 2
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Question
A polygon is convex if, for every pair of points, P and Q belonging to the polygon, the line segment PQ lies completely inside or on the polygon.Which one of the following is NOT a convex polygon?
Correct answer
(A) [figure]
Solution
A polygon is convex if the segment joining any two of its points stays inside or on the polygon; equivalently, every interior angle is less than .
- (A) is a chevron (arrow) shape. Its notch on the left side has a reflex interior angle (greater than ): take one point on the upper arm and one on the lower arm near the left edge; the segment joining them passes through the notch, outside the polygon. So (A) is not convex.
- (B) is a triangle, which is always convex.
- (C) is a square, which is convex.
- (D) is a trapezium, all of whose interior angles are less than , so it is convex.
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