An isosceles trapezium with its inscribed circle. If the lengths are such that b-a=c-b=d-c, what is a : b : c : d?

# Tag: length

## The bear trap

A semicircle with two tangents and a perpendicular line segment from a tangency point. What is the blue area in terms of lengths a and b?

## The road less traveled

What is the area of the trapezium in terms of lengths a and b?

## The hand fan

Three congruent triangles constitute a quadrilateral. What’s red : blue?

## The triple airbag

A triangle containing three tangent semicircles with diameters a, b and c. Three line segments pass through the red tangency points. What is the triangle perimeter?

## At navel level

Two equilateral triangles share a vertex. The centre of the larger one is aligned with the midpoint of a side of the smaller one. What is green : red?

## The common focus

A parabola, its symmetry axis and a tangent. Yellow connects the focus to the intersection point. Red connects the focus to the tangency point. What’s yellow : red?

## The purple hat

A circle with three tangents forming an isosceles triangle. Two tangency points are shown. What is the proportion green : red?

## Two hemispheres

A triangle with its circumscribed circle and a smaller intersecting circle. The two intersection points and the circumcentre are shown. What’s the proportion red : green?

## The wedge

A trapezium with its inscribed circle. Two tangency points are shown. What’s red / blue – yellow / green?