# Mathematical Questions and Solutions in Continuation of the Mathematical Columns of "The Educational Times" Volume 57

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1892 edition. Excerpt: ...the pair at that point and cutting the third at right angles. Show that these three circles are coaxal. S7lution by J. C. ST. CLAIR; Professor S'uuum; and others. Let A, B, C be the three circles, and C' the circle having common contact with A, B, and cutting C orthogonally. If we invert from the point common to A, B, C', these circles become three parallel lines a, b, c', (fig.), and 0 becomes a circle a touching a, b, and having its centre on c' (since c, c' are orthogonal), which is therefore equidistant from a and b. The circles A', B "become equal circles touching b, c and a, c respectively, and having their centres on a, b respectively. It is evident from the original figure that A', B' must intersect; and it is also evident that the intersections of their tangente qui le touche en E. Demontrer que la droite DE passe par un point fixe. into an expression symmetrical with respect to A, B, 0. It is clear that cos B cos %C is a factor. Therefore, if the expression is symmetrical, cos %A is also afactor. Dividing by cos %A cos 1;B cos C, the other factor is 9299. (A. G0RDoN.)--If a polygon of n sides be inscribed in a circle, with vertices A, A, AS A, (taken in order), prove that the following conditions must be satisfied: --8919, (W. J. GnnnNsTnER-r, M.A.)--In the ambiguous case, if A be given angle, a, c given sides (c 11), Ci, C, the two positions of the angular point opposite c, show that the radius of nine-point circle of ABC, C, is half that of nine-point circle of AABC2 if c = 2a, and is equal to radius of inscribed circle of BC, C, if sin A = / 3. 2041, (The late Professor VoLsTENHoLME, D.Sc.)--The whole perimeter (2a) and one side (cents) are given. Prove thashow more

## Product details

• Paperback | 32 pages
• 189 x 246 x 2mm | 77g
• United States
• English
• black & white illustrations
• 1236859022
• 9781236859020