Circle Geometry Problems: Finding Radii and Tangents

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SUMMARY

The discussion focuses on solving specific circle geometry problems involving radius and tangents. The first problem requires finding the radius of a circle that fits in the corner of a page, given point A's coordinates. The second problem involves two circles touching at point A with a common tangent BC, proving that the radius of a smaller circle is one-fourth that of the larger circles. Additionally, the distance from point P to point D in a rectangular room is explored, based on given distances to points A, B, and C.

PREREQUISITES
  • Understanding of circle equations in coordinate geometry
  • Knowledge of tangent properties in circle geometry
  • Familiarity with geometric proofs involving circles
  • Basic skills in solving distance problems in a rectangular coordinate system
NEXT STEPS
  • Study the equation of a circle in the form (x - x0)² + (y - y0)² = r²
  • Learn about the properties of tangents to circles and their relationships
  • Explore geometric proofs related to circle radii and tangents
  • Investigate distance formulas in coordinate geometry for various shapes
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Students studying geometry, educators teaching circle properties, and anyone seeking to improve their problem-solving skills in geometric contexts.

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Man...I hate geometry...I feel like :mad: when I see them...

I can still do them but I can't do these :sick: .

Please help me and diagrams would be nice ;) .

A circle is drawn so that it just fits in the corner of a page. Point A is 1cm from one edge of the page and 2cm from another edge. Find the radius of the cricle.

Two circles of the same radius touch at A and have a common tangent BC. A small circle touches the larger circles and also has BC as a tangent. Prove that the radius of the small circle is 1/4 of the radius of the larger circles.

P is a point within a rectangular room ABCF. P's distance to A, B and C is 4m, 3m and 2m respectively. Find distance DP.
 
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heldensheld said:
Man...I hate geometry...I feel like :mad: when I see them...

I can still do them but I can't do these :sick: .

Please help me and diagrams would be nice ;) .

A circle is drawn so that it just fits in the corner of a page. Point A is 1cm from one edge of the page and 2cm from another edge. Find the radius of the cricle.

Two circles of the same radius touch at A and have a common tangent BC. A small circle touches the larger circles and also has BC as a tangent. Prove that the radius of the small circle is 1/4 of the radius of the larger circles.

P is a point within a rectangular room ABCF. P's distance to A, B and C is 4m, 3m and 2m respectively. Find distance DP.



Ah...****.

Not for homework...Mine isn't exactly homework tho...

Ah well...Mods can delete this if they want :frown: !
 
Hint for the first one: what is the equation for a circle centered at (x0, y0)?

If the circle is in the bottom right corner of the page, and the bottom right of the page is (0,0), what are the coordinates for (x0, y0), the point where the circle will be centered? (you should use r, the radius)

Can you plug in this center position and x=1, y=2 to your equation and solve for r?

Without referring to your formula for r, can you explain why there are two values of r which cross the point (1,2)?
 
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