geometry puzzles

Tag: proportion

The steam locomotive

Two tangent circles, a chord towards the tangency point and a tangent. What’s the proportion a : b in terms of radii R and r?

Beginner

In this right triangle, if red = blue, what is orange : purple?

Beginner

Three semicircles and a circle. Three centres are shown in green. What’s the proportion red : blue?

Two squares share a vertex. One line segment connects their centres, another two vertices. What is the length proportion blue : red?

Five equidistant parallel line segments. What’s the proportion green : red?

Two squares share a vertex. What’s the proportion x : y in terms of side lengths a and b?

Beginner

A square divided by three line segments. What’s the proportion yellow : purple?

Beginner

A square containing two overlapping equilateral triangles. What’s the length proportion a : b?

Five circles, of which the green circles are congruent and so are the blue ones. If r_blue : r_green= 6, what’s r_red : r_green?

Beginner

Two congruent triangles are placed as shown. A line segment passes through the centroid of the yellow triangle. What’s the proportion a : b?