UNDERSTANDING SHAPES (Including Polygons)
161. Curves & Regions · Open, closed, and simple closed curves
P is inside when distance from center < radius; P is outside when distance ≥ radius.
A closed curve forms a complete loop with no endpoints (like a circle). An open curve has two distinct endpoints that do not meet (like an arc). A simple closed curve is a special type of closed curve that does not intersect itself — the boundary is a single continuous loop.
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For subscribers · Selina ICSE: UNDERSTANDING SHAPES (Including Polygons)
What this lesson covers
Try to break it
Drag point P inside and outside the closed curve. When P is inside the curve, it shows 'Interior Point'. When P moves outside, it shows 'Exterior Point'.
How you build it
Draw a closed curve and mark interior, boundary, and exterior points.
- Draw a closed curve (a circle).
The proof, step by step
Prove that P is inside the closed curve when its distance from the center is less than the radius.
- A point is inside the closed curve if its distance from the center is less than the radius.
- A point is outside the closed curve if its distance from the center is greater than the radius.
Worked example
What determines whether point P is inside or outside the closed curve?
A point is inside if its distance from the center is less than the radius, and outside if its distance is greater than or equal to the radius.
- The color of the point
- Distance from the center vs. the radius — correct
- The size of the curve
- The shape of the curve