98. Inscribe in a given circle a polygon all whose sides pass through given points.
99. If two circles X, Y be so related that a triangle may be inscribed in X and circumscribed about Y , an infinite number of such triangles can be constructed.
100. In the same case, the circle inscribed in the triangle formed by joining the points of contact on Y touches a given circle.
101. And the circle described about the triangle formed by drawing tangents to X, at the angular points of the inscribed triangle, touches a given circle.
102. Find a point, the sum of whose distances from three given points may be a minimum.
103. A line drawn through the intersection of two tangents to a circle is divided harmonically by the circle and the chord of contact.
104. To construct a quadrilateral similar to a given one whose four sides shall pass through four given points.
105. To construct a quadrilateral, similar to a given one, whose four vertices shall lie on four given lines.
106. Given the base of a triangle, the difference of the base angles, and the rectangle of the sides; construct the triangle.
107. ABCD is a square, the side CD is bisected in E, and the line EF drawn, making the angle AEF = EAB; prove that EF divides the side BC in the ratio of 2 : 1.