# Calendar: 1899-1900 Page 762

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cx FACULTY OF SCIENCE equidistant from the extremities of the other prove that the projections of the opposite sides on the second diagonal are equal 11 Shew how to connect the Trigonometrical ratios of with those of 180 and 90 and find pairs of solu- tions of the equations sin 30 φ sin θ sin θ 2φ cos φ 12 If Jx cos θ φ cos and χ sin θ sin φ find cos φ and tan Θ Plasmatics Kcamettg &c Candidates are expected to select their questions as follows Queen's Scholars Year Questions 1-6 Queen Scholars II and III Years Questions 5-10 Candidates for the London university Intermediate Exami- nation Questions 5-12 Candidates for Preliminary Certificate in Engineering ac Any Questions Candidates for the Special Matric Certificate in Engineering &c Questions 1-3 Candidates for Certificates of Distinction and Merit may answer any of the Questions Prove that parallelograms on the same base and between the same parallels are equal in area If the area of triangle be given prove that the sum of its sides is least when it is equilateral straight line is divided equally and also unequally Prove that the rectangle contained by the unequal parts and the square on the line between the points of section are together equal to the square on half the line From any point in the base BC of an equilateral triangle ABC parallels are drawn to the sides meeting them in the points Ε and Prove that the sum of the squares on DE DF and BC is equal to twice the square on AD Prove that angles in the same segment of circle are equal Through the middle point of fixed chord of circle any other chord is drawn Prove that the tangents at its ex-

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