Categories
Intermediate

The side mirror

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

Categories
Advanced

The inner parallel

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

Categories
Intermediate

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.

Categories
Intermediate

The hand fan

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

Categories
Intermediate

The queen

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

Categories
Beginner

The leftward lean

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

Categories
Intermediate

We are equal

A quadrilateral with its diagonals. What’s the angle α?

Categories
Advanced

The square of Amaresh

A right triangle having semicircles along its perpendicular sides and two smaller inscribed circles. Prove that the orange quadrilateral is a square.

Categories
Beginner

The French kiss

Two tangent circles and two red tangent line segments. The three tangency points are shown. What is the angle β in terms of the angle α?

Categories
Intermediate

Similar intention

A cyclic quadrilateral and two diagonals. What fraction of its area is blue?