117. The product of the bisectors of the three angles of a triangle whose sides are a, b, c, is
118. In the same case the product of the alternate segments of the sides made by the bisectors of the angles is
119. If three of the six points in which a circle meets the sides of any triangle be such, that the lines joining them to the opposite vertices are concurrent, the same property is true of the three remaining points.
120. If a triangle A′B′C′ be inscribed in another ABC, prove
is equal twice the triangle A′B′C′ multiplied by the diameter of the circle ABC.
121. Construct a polygon of an odd number of sides, being given that the sides taken in order are divided in given ratios by fixed points.
122. If the external diagonal of a quadrilateral inscribed in a given circle be a chord of another given circle, the locus of its middle point is a circle.