21. Give an example of two triangles inversely similar. Ans. If two lines passing through any point O outside a circle intersect it in pairs of points A, A′; B, B′, respectively, the triangles OAB, OA′B′, are inversely similar.
22. What point is it round which a figure can be turned so as to bring its sides into positions of parallelism with the sides of a similar rectilineal figure. Ans. The centre of similitude of the two figures.
23. How many figures similar to a given rectilineal figure of sides can be described on a given line?
24. How many centres of similitude can two regular polygons of n sides each have? Ans. n centres, which lie on a circle.
25. What are homothetic figures?
26. How do the areas of similar rectilineal figures vary?
27. What proposition is xix. a special case of?
28. Define Philo’s line.
29. How many centres of similitude have two circles?
Exercises on Book VI.