19. Upon the segments AC, CB of a line AB equilateral triangles are described: prove that if D, D′ be the centres of circles described about these triangles, 6DD′2 = AB2 + AC2 + CB2.
20. If a, b, p denote the sides of a right-angled triangle about the right angle, and the perpendicular from the right angle on the hypotenuse,
+
=
.
21. If, upon the greater segment AB of a line AC, divided in extreme and mean ratio, an equilateral triangle ABD be described, and CD joined, CD2 = 2AB2.