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  • ...A</math>, via the [[inscribed angle theorem]], their circumcenters are the midpoints of the side lengths of <math>\triangle ABC</math>, which we know to be on t
    8 KB (1,408 words) - 08:39, 10 July 2024
  • Let <math>D</math> and <math>E</math> be midpoints of <math>BC</math> and <math>NC</math> respectively.
    3 KB (496 words) - 12:35, 18 January 2023
  • The median of a trapezoid is defined as the line connecting the midpoints of the two legs. Its length is the arithmetic mean of that of the two bases
    1 KB (246 words) - 09:54, 2 January 2024
  • * the segment joining the midpoints of the bases is perpendicular to the bases
    577 bytes (81 words) - 09:33, 18 April 2019
  • ...f quadrilateral <math>ABCD</math>. The quadrilateral formed by joining the midpoints of <math>\overline{AB}</math>, <math>\overline{BC}</math>, <math>\overline{
    13 KB (1,957 words) - 11:53, 24 January 2024
  • ...ngle XOY = 90^{\circ}</math>. Let <math>M</math> and <math>N</math> be the midpoints of legs <math>OX</math> and <math>OY</math>, respectively. Given that <math
    10 KB (1,547 words) - 03:20, 9 October 2022
  • Now, we look for any additional equilateral triangles. Connecting the midpoints of three non-adjacent, non-parallel edges also gives us more equilateral tr
    4 KB (495 words) - 00:36, 26 May 2024
  • ...{\frac{1}{4}\left(x^2+y^2\right)}=\sqrt{\frac{1}{4}(4)}=1</math>. Thus the midpoints lying on the sides determined by vertex <math>(0,0)</math> form a quarter-[ ...rter circle at each corner of the square. The area enclosed by all of the midpoints is <math>4-4\cdot \left(\frac{\pi}{4}\right)=4-\pi \approx .86</math> to th
    4 KB (647 words) - 20:51, 12 January 2025
  • ...have length 2 and whose endpoints are on adjacent sides of the square. The midpoints of the line segments in set <math> S </math> enclose a region whose area to
    9 KB (1,434 words) - 12:34, 29 December 2021
  • ...h>, as shown in the figure. Let <math>d</math> be the distance between the midpoints of edges <math>AB</math> and <math>CD</math>. Find <math>d^{2}</math>.
    7 KB (1,045 words) - 00:18, 5 January 2025
  • 7 KB (1,084 words) - 01:01, 28 November 2023
  • ...> and <math>(16,24).</math> The vertices of its midpoint triangle are the midpoints of its sides. A triangular pyramid is formed by folding the triangle along
    7 KB (1,094 words) - 12:39, 16 August 2020
  • ...th>100</math> units longer than the other base. The segment that joins the midpoints of the legs divides the trapezoid into two regions whose areas are in the r
    6 KB (947 words) - 20:11, 19 February 2019
  • Given a triangle, its midpoint triangle is obtained by joining the midpoints of its sides. A sequence of polyhedra <math>P_{i}</math> is defined recursi
    8 KB (1,282 words) - 20:12, 19 February 2019
  • ...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 <math>P</math>, wit We consider the locus of midpoints of the chords from <math>A</math>. It is well-known that this is the circle
    20 KB (3,497 words) - 14:37, 27 May 2024
  • 3 KB (548 words) - 20:40, 28 June 2024
  • 2 KB (376 words) - 12:49, 1 August 2022
  • ...w a circle of radius 4 around the center of the rectangle. Picking the two midpoints on the sides of length 6 and opposite intersection points on the segments o
    3 KB (601 words) - 08:25, 19 November 2023
  • ...is simply the sum of two [[segment]]s of the circles. If we construct the midpoints of <math>M_1, M_2 = \overline{AB}, \overline{BC}</math> and note that <math
    4 KB (717 words) - 21:20, 3 June 2021
  • 5 KB (884 words) - 13:33, 18 June 2024

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