An elementary treatise on geometry : simplified for beginners not versed in algebra . and therefore these triangles are not only isos-celes, but also equilateral, consequently each of the sidesAB, BC, CD, &.C., of the hexagon is equal to the radiusof the circle. QUERY XVm. If, in a regular inscribedpolygon, you draw from the cen-tre of the circle the radii Oi,Ok, Ol, Om, Sfc, perpendicularto the chords AB, BC, CD, S^c.;and at the extremities of theseradii, the tangents MN, NP,PQ, S^c.; what do you observe with regard to the figure MNPQRS, circumscribed aboutthe circle 1 A. The figure MNPQRS, c
An elementary treatise on geometry : simplified for beginners not versed in algebra . and therefore these triangles are not only isos-celes, but also equilateral, consequently each of the sidesAB, BC, CD, &.C., of the hexagon is equal to the radiusof the circle. QUERY XVm. If, in a regular inscribedpolygon, you draw from the cen-tre of the circle the radii Oi,Ok, Ol, Om, Sfc, perpendicularto the chords AB, BC, CD, S^c.;and at the extremities of theseradii, the tangents MN, NP,PQ, S^c.; what do you observe with regard to the figure MNPQRS, circumscribed aboutthe circle 1 A. The figure MNPQRS, circumscribed about thecircle, is a regular polygon, of the same number of sidesas the inscribed polygon, ABCDEF. Q. How can you prove this ? A. The chords AB, BC, CD, &,c., are perpendicularto the same radii, to which the tangents MN, NP, PQ,&c., are perpendicular; consequently the chords AB, BC,CD, &c., are parallel to the tangents MN, NP, PQ, «S^c.(for two straight lines, which are both perpendicular to athird line are parallel to each other; Query 7, Sect. I.);. 118 GEOMETRY. and therefore the triangles ABO, BCO, CDO, &,c., areall similar to the triangles MNO, NPO, PQO, &, fromwhich they may be considered as cut off, by the linesAB, BC, CD, &LC. being drawn parallel to the sides MN,NP, PQ, &c. (auery 16, Sect. II.) Now, as the trian-gles ABO, BCO, CDO, 6lc., are all equal to one another,the triangles MNO, NPO, PQO, &c., are all equal toone another. And therefore the circumscribed figureMNPQRS is a regular polygon, similar to the one in-scribed in the circle.
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Keywords: ., bookauthorgrundfrancisjfrancisjoseph18051863, bookcentury1800
