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

# Tag: 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.

## The skyscraper

A blue parallelogram with an extended diagonal. What is the proportion green : orange?

## The first cut

Using one straight cut, divide this triangle in two pieces. Paste them together to form a parallelogram with perimeter 19.

## The balance sheet

A unit square and a parallelogram. What’s the area of the latter?