Two congruent circles and a right triangle inside a semicircle. What fraction is blue?

# Tag: triangle

## The tin foil hat

A circle inside a quarter circle. The triangle connects the two tangency points and the top of the quarter circle. What’s the angle α?

## The hammock

A square inscribed in a triangle. Two areas are given. What is the square’s area?

## The twin triangles

Two squares share a vertex. Prove that the red triangle is congruent to the blue one.

## Ice cube

A rectangle and a square. What is the proportion purple : blue?

## The hourglass

A rectangle with two crossing line segments. What’s the minimal shaded fraction?

Four quarter circles of radius 1, each containing a square. What is the blue area?

## Below the tree line

A triangle is split in two. What is the area of the green quadrilateral in terms of lengths a and b?

## Tympanum II

A regular pentagon with a diagonal. What is the top angle of the isosceles triangle?

## The ramp

A right triangle is split in two. What is the maximum yellow fraction?