Circle Geometry: Determining When a Point Lies Outside the Circle Based on Radius

Circle Position with Distance Comparison

A point whose distance from the center of the circle is _______ than the radius, is outside the circle.

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Step-by-step written solution

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1

Understand the problem

A point whose distance from the center of the circle is _______ than the radius, is outside the circle.

2

Step-by-step solution

Let's remember that the circle is actually the inner part of the circumference, meaning the enclosed area within the frame of the circumference.

Therefore, a point whose distance is greater than the center of the circle will necessarily be outside the circle.

3

Final Answer

greater

Key Points to Remember

Essential concepts to master this topic
  • Rule: Points outside circles have distances greater than radius
  • Technique: Compare distance from center: if d > r, point is outside
  • Check: Verify distance calculation and compare correctly to radius value ✓

Common Mistakes

Avoid these frequent errors
  • Confusing 'greater than' with 'less than' relationships
    Don't think points closer to center are outside = backwards logic! This confuses the fundamental definition of circles. Always remember: distance greater than radius means outside, distance less than radius means inside.

Practice Quiz

Test your knowledge with interactive questions

A point whose distance from the center of the circle is _______ than the radius, is outside the circle.

FAQ

Everything you need to know about this question

What happens when the distance exactly equals the radius?

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When the distance from center equals the radius, the point lies on the circle itself (the circumference). It's neither inside nor outside!

How do I calculate the distance from a point to the center?

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Use the distance formula: d=(x2x1)2+(y2y1)2 d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} where (x₁,y₁) is the center and (x₂,y₂) is your point.

Can a circle have negative radius?

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No! Radius is always a positive distance. If you get a negative value in calculations, check your work - you might have made an error.

What's the difference between a circle and its circumference?

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The circumference is just the boundary (the curved line). The circle includes all points inside this boundary plus the boundary itself.

Why is this concept important in geometry?

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Understanding point positions relative to circles helps with coordinate geometry, finding intersections, and solving real-world problems involving circular regions and boundaries.

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