3. Describe a circle passing through a given point, having its centre on a given line and touching a given circle.
4. Describe a circle through two given points, and intercepting a given arc on a given circle.
5. A, B, C, D are four collinear points, and EF is a common tangent to the circles described upon AB, CD as diameters: prove that the triangles AEB, CFD are equiangular.
6. The diameter of the circle inscribed in a right-angled triangle is equal to half the sum of the diameters of the circles touching the hypotenuse, the perpendicular from the right angle of the hypotenuse, and the circle described about the right-angled triangle.
Questions for Examination on Book III.
1. What is the subject-matter of Book III.?
2. Define equal circles.
3. What is the difference between a chord and a secant?
4. When does a secant become a tangent?
5. What is the difference between a segment of a circle and a sector?