Interior consists of points strictly inside a boundary; exterior consists of points strictly outside the boundary.
A closed fence divides the world into two zones: the yard inside and everything else outside. Any closed curve does the same—splitting the plane into an interior region and an exterior region.
Showing a random 20 of 50 problems.
Example 1
easy
Point P is 7 units from center of a circle with radius 5. Is P inside or outside?
Example 2
medium
Is the point (−2,−3) inside the circle of radius 4 centered at the origin?
Example 3
challenge
Why does the boundary belong to neither the interior nor the exterior, making three distinct categories?
Example 4
medium
For the circle (x+1)2+(y−2)2=49, is (2,5) interior?
Example 5
easy
A point is 2 units from the center of a circle of radius 5. Is it interior or exterior?
Example 6
challenge
Is the point (6,8) interior, on, or exterior to the circle (x−2)2+(y−3)2=36?
Example 7
hard
A square room of side 10 has a smaller square pillar of side 2 in the exact center. A point sits 4 units from the room's center. Is it interior to the walkable region?
Example 8
medium
Inside a hexagonal park, a child stands at the geometric center. Interior or exterior to the park's boundary?
Example 9
hard
Is the point (1,1) in the interior of the region defined by x+y<3 AND x2+y2<5?
Example 10
easy
A point is exactly 5 units from the center of a circle of radius 5. Where is it?
Example 11
hard
A point P=(3,2) and a circle centered at (1,1) with radius r=3. Is P interior or exterior to the circle? Show your work using the distance formula.
Example 12
medium
A rectangle has vertices at (0,0), (4,0), (4,3), and (0,3). Determine whether the point (2,1.5) is interior, exterior, or on the boundary of the rectangle.Rectangle with vertices (0,0), (4,0), (4,3), (0,3) — is (2, 1.5) inside?
Example 13
challenge
A donut shape (annulus) has inner radius 2 and outer radius 5. Where is the point (3,4)? (Centered at origin.)
Example 14
easy
Inside a square room, are you in the interior or exterior of the square?
Example 15
easy
A point is 8 units from the center of a circle of radius 5. Interior or exterior?
Example 16
challenge
A maze is drawn as a single wiggly closed curve. A treasure dot is somewhere in the picture. How can you tell if it's inside the curve without tracing the whole maze?
Example 17
medium
Why is the interior of a circle called an 'open' region, while including the boundary makes it 'closed'?
Example 18
hard
A triangle has vertices (0,0),(4,0),(2,3). Is (2,1) interior?Triangle with vertices (0,0), (4,0), (2,3) — is (2,1) an interior point?
Example 19
hard
A circle is described by the inequality (x−2)2+(y−3)2≤16. Describe the interior as a strict inequality.
Example 20
hard
Is the point (0,0) in the interior, on, or exterior to the parabola region y≥x2?