Calendar: 1896-1897 Page 691

FACULTY OF SCIENCE ci secant he drawn then 1110 rectangle contained by the whole secant and the part of it without the circle shall be equal to the square on the tangent The vertical angle BAC of triangle is bisected bv straight line which cuts the base at and the circumscribing circle at prove that the rectangle ΕΠ ΕΛ is equal to the square on Eli Describe an isosceles triangle having each of the angles at the base double the anglo at the vertex In Euclid's figure for this proposition there is triangle circumscribed by circle prove that the middle point certain arc of this circle is the centre of the circle circum- scribing another triangle in the figure The diameter of halfpenny is one inch six of these coins are placed with their centres at the corners of regular hexagon which is of such size that adjacent coins touch find the area of that portion of the hexagon which is 1111 covered by the coins Λ circle having diameter fifteen inches is divided into two segments by chord whose length is double its distance from the centre find the area of each segment Nflfo νι χι Υ Κ Λ II ft Prove that equiangular triangles arc similar In an isosceles triangle AI whose base is the bisector of the angle meets All in E$ and perpendicular to BO at Β in Shew that DE EC BC the perimeter of the triangle Define compound ratio and duplicate ratio Prove that similar triangles are to one another in the duplicate ratio of their homologous sides ABC is any triangle two circles intersecting at are described touching BC at Β and respectively Prove that their diameteis are in the duplicate ratio of Β to AC 10 The rectangle contained by the diagonals of quadri- lateral inscribed in circle is equal to the sum of the two rectangles contained by its opposite sides If an equilateral triangle be inscribed in circle and its angular points be joined to any point on the circumference