A parallelogram and four equilateral triangles. What is yellow : green?

# Tag: parallelogram

## Pink parallels

A pink parallelogram with two extended sides. What’s α : β?

## Three’s a crowd

Four equilateral triangles. Prove that the red quadrilateral is a parallelogram.

## The gyroscope

Two ellipses go through each others focal points. Prove that the focal points are the vertices of a parallelogram.

## The beam in your eye

Three parallelograms are inscribed in a circle. Prove that the common red vertex is the orthocentre of the dashed triangle.

## The iron curtain

A parallelogram ABCD with a circle and a diameter CE. Prove that point E is the orthocentre of triangle ABD.

## The crazy quilt

A parallelogram is divided into several areas. What is the area X of the blue trapezium?

## Out of proportion

An equilateral triangle containing a parallelogram, another equilateral triangle and a circular arc that is tangent in its base vertices. What is the proportion pink : blue?

## Silent circle

A large triangle with one side tangent to a circle. The tangency point is the vertex of a blue parallelogram. What is the red area?

## The orange belt

Three squares and three shared vertices. Prove that the orange quadrilateral is in fact a parallelogram.