Two squares sharing a vertex. Two vertices are connected by a line segment. What is yellow : green?

# Tag: length

## Holes in my heart

The heart is divided into right triangles, each of which contains a blue circle. What is the total circumference of the blue circles in relation to the green perimeter and the lengths of the purple and orange lines in the centre?

Some chords and segments inside a semicircle. What is the ratio of red to blue?

## The basketball court

An orange circle is squeezed inside a rectangle. Show that no matter how the blue point moves on the circle, the derived points Q and P will satisfy |QL| = |KP|.

## Wheel of fortune

A unit square and a point on the inscribed circle. What is a^{2}+b^{2}+c^{2}+d^{2}?

## The see-through triangle

A regular hexagon and an equilateral triangle share a vertex. What is red : blue?

A triangle with two line segments. What’s the angle α?

The red and green wedges subtend the same angle, there are two right angles, and the blue sides have the same length. What is the ratio of lengths of the green and red segments?

## Downhill skiing

Choose any point D on the side AB of an isosceles triangle ABC, then extend the side AC beyond C to a point F with |CF| = |DB|. Show that the segment DF is cut exactly in two by the third side BC—that the orange and red trails are equal.

## Corner pursuit

Four corners of a square pursue each other clockwise, and after each unit step mark out the new smaller square. Show that the squares sizes in the sequence decrease in size to 1 in the limit.