Mathematical Questions with Their Solutions, from the "Educational Times" Volume 36
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Mathematical Questions with Their Solutions, from the "Educational Times" Volume 36

Mathematical Questions with Their Solutions, from the "Educational Times" Volume 36


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1883 Excerpt: ...AABC when its inscribed circle (or its radius QE) is a maximum. 6864. (By Professor Hudson, M.A.)--If I, O he the centres of the inscribed and circumscribed circles of a spherical triangle, r, R their radii, and '2a = a + b + c, prove that 2 sin a cos I0 = (sin a + sin i + siu c) cos r cos R. 6878. (By T. C. Simmons, M.A.)--If A, B are two points in the plane of a given circle; give a geometrical construction for finding the position of a point P on the circumference, such that the lines Al', BP make equal angles with the tangent at P. Solution by Dr. Curtis; 'E. Euttee; and others. This, which is known as Alrazen's problem, admits of the following geometrical solution: --If C be the centre of the circle and a its radius, take E and F so that AC. CE = a- = BC. CF; draw the hyperbola-locus of vertex of all triangles whose common base is EF, and the difference of whose base angles = L CEF CFE; let H be any one of the four points in which this hyperbola cuts the circle; then, as ZEFH-FEH-CEF-CFE, we have LCEH = CFH, and in the triangles ACH, HCE, we have AC: CH = CH: CE, therefore / AHC = CEH; similarly L BHC = CFH, and therefore L AHC = BHC, and / AHK = BHK, therefore H ia one of the required points. 6924. (By Professor Seitz, M.A.--Atriangleis formed by joining three random points within a sphere; prove that the average area (1) of the triangle is T9, -r2, and (2) of its inscribed circle is (f f j--$f log 2) irr2. 6017. (By J. L. Mckbnzib, B.A.)--A straight line XY cuts the tangents at two given points A and B on a given circle in L and M respec tively, and the circlo itself in C and D; then (1) if the circles ABL, ABM cut XY in a and $ respectively, prove Ca = D&; and (2) if the circles passing through L and M, and touching the given circle in B...


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Product Details
  • ISBN-13: 9781236384461
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 30
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1236384466
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 73 gr


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