Calendar: 1875-1876 Page 587

GENERAL LITERATURE AND SCIENCE 58 which this line makes with the line touching the circle shall be equal to the angles which are in the alternate segments of the circle If from any point in the circumference of circle chord and tangent be drawn the perpendiculars dropped on them from the middle point of the subtended arc are equal to one another To describe square about given circle Show that no rectangle but square can be described about circle 10 To inscribe an equilateral and equiangular hexagon in given circle Any equilateral figure which is inscribed in circle is also equiangular 11 The area of triangle is equal to half the rectangle of its base and altitude Perpendiculars are drawn from any point within an equilateral triangle on the three sides shew that their sum is constant 12 The rectangle contained by tbe diagonals of quadri- lateral figure inscribed in circle is equal to both the rectangles contained by its opposite sides 13 Show that the equation Ax By always repre- sents straight line and interpret the equation Ay'- Bxy -j- Car2 Shew that 3y2 8xy 'J 30 27 represents two straight lines at right angles to one another 14 Express the area of triangle in terms of the coordinates of its angular points Draw the lines whose equations are respectively -f- 1y 1x andy χ and find the area of the triangle they form 15 The straight lines drawn from the angles of triangle to the middle points of the opposite sides meet at point 16 Find the equation to circle referred to any oblique axes What does this become when the origin is on tbe perimeter the axes are inclined at an angle of 20 and the parts of them intercepted by the circle are and 17 Prove that the angle in semicircle is right angle 18 Prove that in the parabola ST SP