A quarter circle with two chords of given length. What is the area of the orange quadrilateral?

# Tag: quadrilateral

## Sailing by night

A circle with an inscribed quadrilateral. Prove that ab=cd. Kindly provided by Marshall W. Buck.

## The manta ray

A quadrilateral with connected side midpoints. What’s blue : red : yellow?

## Crossing mountains

A rectangle with four line segments. What’s brown : blue?

## The side mirror

An isosceles triangle and an external point with three line segments. Prove that the red points form a cyclic quadrilateral.

## The inner parallel

A cyclic quadrilateral with its diagonals and two altitudes. Prove that AB is parallel to EF.

## Ceteris paribus

Three circles with their centres and a triangle ABC. Given that D is the midpoint of BC, prove that quadrilateral ABEF and triangle ECF have both equal perimeter and equal area.

## The hand fan

Three congruent triangles constitute a quadrilateral. What’s red : blue?

## The queen

A cyclic quadrilateral with extended sides and two tangents forming an angle γ. What is γ in terms of α and β?

## The leftward lean

Two triangles form a quadrilateral. What’s the total orange area?