The First Six Books of the Elements of Euclid

by Euclid; John Casey

30. Place a given triangle so that its three sides shall pass through three given points.

31. Place a given triangle so that its three vertices shall lie on three given lines.

32. Construct the greatest triangle equiangular to a given one whose sides shall pass through three given points.

33. Construct the least triangle equiangular to a given one whose vertices shall lie on three given lines.

34. Construct the greatest triangle equiangular to a given one whose sides shall touch three given circles.

35. If two sides of a given triangle pass through fixed points, the third touches a fixed circle.

36. If two sides of a given triangle touch fixed circles, the third touches a fixed circle.

37. Construct an equilateral triangle having its vertex at a given point, and the extremities of its base on a given circle.

38. Construct an equilateral triangle having its vertex at a given point, and the extremities of its base on two given circles.

39. Place a given triangle so that its three sides shall touch three given circles.