Ratio and proportion

Equal touching circles have centres on a line. From a point of this line on a circle, a tangent is drawn to the farthest circle. Find the lengths of chords where the line cuts the other circles.

Draw any triangle PQR. Find points A, B and C, one on each side of the triangle, such that the area of triangle ABC is a given fraction of the area of triangle PQR.

In this question we push the pH formula to its theoretical limits.

Can you work out the fraction of the original triangle that is covered by the green triangle?

Investigate some of the issues raised by Geiger and Marsden's famous scattering experiment in which they fired alpha particles at a sheet of gold.

Solve an equation involving the Golden Ratio phi where the unknown occurs as a power of phi.

Show that it is rare for a ratio of ratios to be rational.