74. If two sides of a triangle be given in position, and if the area be given in magnitude, two points can be found, at each of which the base subtends a constant angle.
75. If a, b, c, d denote the sides of a cyclic quadrilateral, and s its semiperimeter, prove its area =
.
76. If three concurrent lines from the angles of a triangle ABC meet the opposite side in the points A′, B′, C′, and the points A′, B′, C′ be joined, forming a second triangle A′B′C′,
77. In the same case the diameter of the circle circumscribed about the triangle ABC = AB′.BC′.CA′ divided by the area of A′B′C′.
78. If a quadrilateral be inscribed in one circle, and circumscribed to another, the square of its area is equal to the product of its four sides.
79. If on the sides AB, AC of a triangle ABC we take two points D, E, and on their line of connexion F, such that
