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  Item Reference: KCLCAL-1893-1894-837

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faculty of science CXV fuditJ VI XL YEAR II Shew how to inscribe regular pentagon in given circle li ABODE be the pentagon and AB produced meet DC produced in prove that the triangle FCB is equal to the triangle DAB in all respects If two triangles are equiangular the sides about the equal angles are proportionals Two circles intersect at and PAQ pAq are two straight lines drawn through and terminated by the two circles prove that Ρ Β BQ pB Bq 10 If OA OB OC be three straight lines passing through point Ο shew how to draw straight line cutting them in and so that PQ may be to QR in given ratio 11 Shew how to draw perpendicular to given plane from given point without it If each of two intersecting edges of tetrahedron be per- pendicular to its opposite edge shew that the remaining pair of opposite edges are perpendicular to each other 12 The areas of the sections of pyramid made by planes parallel to the base are proportional to the squares of their distances from the vertex 13 In parabola the subtangent is double the abscissa and the subnormal is equal to the semi-latus-rectum The abscissa AN of point Ρ on parabola is equal to the latus-rectum AR is straight line passing through the vertex and the extremity of the latus rectum on the same side of the axis as and intersecting the tangent at Ρ in If AM be the abscissa of prove that AM is one- third of the latus-rectum 14 wire bent so as to have two parts AB BC at right angles is so constrained that AB always passes through fixed point and Β always lies on fixed straight line shew that BC envelopes parabola
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