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?

Categories
Intermediate

Z

A green quadrilateral of which two sides are tangent to a quarter circle of radius r. What is its area?

Categories
Beginner

The flying saucer

A quarter circle with four chords. What is the proportion purple : gold?

Categories
Advanced

The freight elevator

Four points A, B, C and D form a quadrilateral. Prove that it is a rectangle if and only if for an arbitrary point P we have PA2+PC2=PB2+PD2.

Categories
Intermediate

Brothers in arms

The tangency points of two tangents of a circle are connected. Three perpendiculars are drawn from a point on the circle, of which two have a given length. What’s the proportion red : yellow?