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- A '''parabola''' is a type of [[conic section]]. A parabola is a [[locus]] of points that are equidistant from a point (the [[focus]]) and a line (t ==Problems==3 KB (551 words) - 15:22, 13 September 2023
- A circle is defined as the [[set]] (or [[locus]]) of [[point]]s in a [[plane]] with an equal distance from a fixed point. ==Problems==9 KB (1,585 words) - 12:46, 2 September 2024
- Equivalently, it is defined as the [[locus]], or [[set]], of all [[point]]s <math>P</math> such that the sum of the di ==Problems==5 KB (892 words) - 20:52, 1 May 2021
- ==Problems== ([[2006 AIME I Problems/Problem 14|Source]])6 KB (1,003 words) - 23:02, 19 May 2024
- So the locus of points that can be the center of the circle with the desired properties ...>CF_2=4+r</math>. Therefore, <math>CF_1+CF_2=20</math>. In particular, the locus of points <math>C</math> that can be centers of circles must be an ellipse12 KB (2,001 words) - 19:26, 23 July 2024
- ...hat works is <math>30\cdot \frac {25}{2} = 375</math>, and the area of the locus of all centers of any circle with radius 1 is <math>34\cdot 13 = 442</math> [[Category:Intermediate Geometry Problems]]5 KB (836 words) - 06:53, 15 October 2023
- As with some of the other solutions, we analyze this with a locus—but a different one. We'll consider: given a point <math>P</math> an .../math>, and let <math>AD</math> be a chord of circle <math>O</math>. The [[locus]] of midpoints <math>N</math> of the chord <math>AD</math> is a circle <mat20 KB (3,497 words) - 14:37, 27 May 2024
- An ellipse is defined to be the [[locus]] of points <math>P</math> such that the sum of the distances between <math [[Category:Intermediate Geometry Problems]]5 KB (982 words) - 23:57, 5 December 2024
- ...s that <math>\angle APB, \angle BPC, \angle CPA > 90^{\circ}</math>; the [[locus]] of each of the respective conditions for <math>P</math> is the region ins ...of <math>\triangle ABC</math> from <math>B</math>). Thus, the area of the locus of <math>P</math> (shaded region below) is simply the sum of two [[segment]4 KB (717 words) - 21:20, 3 June 2021
- Problems of the 1st [[IMO]] 1959 in Romania. [[1959 IMO Problems/Problem 1 | Solution]]3 KB (480 words) - 10:57, 17 September 2012
- ...ngth 6^(1/2)*OM. then bisect it for desired length. Next draw the circular locus of points X such that MXO is 45 degrees. To accomplish this, simply find th [[Category:Olympiad Geometry Problems]]6 KB (939 words) - 16:31, 15 July 2023
- (c) Find the locus of the midpoints of the segments <math>PQ </math> as <math>M </math> varies ...., half the length of <math>AB</math>, which is a constant. Therefore the locus in question is a line segment.4 KB (729 words) - 07:23, 23 May 2024
- .../math> is equidistant from <math>X</math> and <math>Y</math>. However, the locus of all points equidistant from <math>X</math> and <math>Y</math> is the pla *[[2006 Romanian NMO Problems]]3 KB (509 words) - 22:22, 15 August 2012
- .../math> is inscribed in the sphere <math>\displaystyle S </math>. Find the locus of points <math>\displaystyle P </math>, situated in <math>\displaystyle S ...ntroid of <math>\displaystyle ABCD </math>, which is therefore the desired locus, Q.E.D.2 KB (346 words) - 13:59, 30 July 2006
- [[1970 Canadian MO Problems/Problem 1 | Solution]] [[1970 Canadian MO Problems/Problem 2 | Solution]]4 KB (604 words) - 03:32, 8 October 2014
- [[2006 Canadian MO Problems/Problem 1 | Solution]] ...h>, and <math>F</math> and <math>G</math> on <math>BC</math>. Describe the locus of the intersections of the diagonals of all possible rectangles <math>DEFG2 KB (338 words) - 12:02, 28 January 2009
- ..., and <math>F</math> and <math>G</math> on <math>BC</math>. Describe the [[locus]] of the [[intersection]]s of the [[diagonal]]s of all possible rectangles The locus is the [[line segment]] which joins the [[midpoint]] of side <math>BC</math2 KB (416 words) - 19:00, 21 September 2014
- Problems of the 2nd [[IMO]] 1960 Romania. [[1960 IMO Problems/Problem 1 | Solution]]3 KB (511 words) - 20:21, 20 August 2020
- ...of <math> \displaystyle A_1 </math> under the spiral similarity. But the locus of <math> \displaystyle A_1 </math> is a circle, and the image of a circle * [[2002 IMO Shortlist Problems]]3 KB (470 words) - 06:32, 28 March 2007
- [[1961 IMO Problems/Problem 1 | Solution]] [[1961 IMO Problems/Problem 2 | Solution]]3 KB (425 words) - 20:18, 20 August 2020