A quadrilateral and a parallelogram share two sides, and a vertex from each determine the orange square. The lengths BC, EF, AD are 4,5,7 respectively, where E and F are midpoints of AB and DC. What is the orange area?

# Tag: parallelogram

## Euclid’s wing

Several line segments, some of which are parallel. What is green : orange?

## Dancing squares

Four squares and one centre. Prove that the red quadrilateral is a parallelogram.

## Triangles galore

Four equilateral triangles. Two centres are shown. Prove that the green quadrilateral is a parallelogram.

## The lighthouse

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

## 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.