# Calendar: 1879-1880 Page 602

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602 GENERAL LITERATURE AND SCIENCE 13 In spherical triangle if Α Β prove that sin2 sin2 sin2 Δ £ XX eomctru Describe square on given straight line The straight lines drawn at right angles to the sides of triangle from the points of bisection of the sides meet at point Describe square equal to given rectilineal figure The opposite angles of any quadrilateral inscribed in circle are together equal to two right angles Prove the converse of the preceding proposition If two straight lines cut one another-within circle the rectangle contained by the segments of the one shall be equal to the rectangle contained by the segments of the other Inscribe regular pentagon in given circle In right-angled triangle if perpendicular be drawn from the right angle to the opposite side the triangles on either side of it are similar to the whole triangle and to one another If from any point in the circumference of the circle described about triangle perpendiculars are drawn to the sides of the triangle the three points of intersection are in the same straight line 10 Express the area of triangle in terms of the co- oidinates of its angular points 11 Draw the lines χ jg and find the area of the triangle formed by them 12 Find the length of the perpendicular drawn from given point upon given straight line 13 Find the perpendicular distance of the point from the straight line

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