miles.
26. Two parallel chords of a circle are 12 perches and 16 perches respectively, and their distance asunder is 2 perches; find the length of the diameter.
27. What is the locus of the centres of all circles touching a given circle in a given point?
28. What is the condition that must be fulfilled that four points may be concyclic?
29. If the angle in a segment of a circle be a right angle and a-half, what part of the whole circumference is it?
30. Mention the converse Propositions of Book III. which are proved directly.
31. What is the locus of the middle points of equal chords in a circle?
32. The radii of two circles are 6 and 8, and the distance between their centres 10; find the length of their common chord.
33. If a figure of any even number of sides be inscribed in a circle, prove that the sum of one set of alternate angles is equal to the sum of the remaining angles.