Calendar: 1896-1897 Page 694

civ FACULTY OF SCIENCE respectively Prove that AY is mean proportional between AX and AO From point Ο within triangle ABC 0Ώ 0E OP are drawn perpendicular to the sides BC CA AB respectively Prove that if the angle FBE is constant the locus of Ο is an arc of circle passing through Β and With one extremity of the diameter AC of circle as centre circle of given radius greater than AC is de- scribed any point of it is joined to and Ρ is the mid-point of BC Prove that the tangent drawn from Ρ to the first circle is of constant length VABC is tetrahedron are the mid- points of BC CA AB VA VB VC respectively Prove that VA2 VB2 FC2 BC2 CA2 AB2 is four times PL2 QE2 RF2 If 12 y2 χ and being finite and positive prove that -f y2 Find number of three digits which is multiplied by by inserting cypher between the tens and hundreds figuies Plcnouraliou YEARS II III ABCB is rectangular piece of paper Ε is point in the side AD inches from and inch from When the paper is folded along the line BE it is found that the corner falls exactly on the edge DC Find thc area of the portion BCDE 10 Out of circular cylinder of lead 12 inches high is cut right circular cone of the same height on the same base The remaining portion of the lead is melted and used to continue the cone from the base Find the heigh of the new cone so formed 11 Find the volume of wedge of height 11 included between rectangle sides and straight line length parallel to If 45 ft 30 ft express the volume in cubic yards 12 Prove that the surface of zone of sphere included between two parallel planes is equal to the surface included between thes3 planes of the zone of right circular circum-