Two congruent circles and a right triangle inside a semicircle. What fraction is blue?

# Category: Advanced

## The orange belt

Three squares and three shared vertices. Prove that the orange quadrilateral is in fact a parallelogram.

## Tympanum II

A regular pentagon with a diagonal. What is the top angle of the isosceles triangle?

## The tympanum

A regular pentagon with a diagonal and an extended side. What is the top angle of the isosceles triangle?

## Points of authority

Three squares and three shared vertices. Prove the three red vertices are collinear.

## The balancing block

A rectangle inside a square. One of its sides is tangent to the quarter circle. What fraction is green as x approaches 0?

## Spider-Man

A circle with four chords. Two chord lengths are given. What is the circle area?

## The fallen pine

Two congruent isosceles triangles and three lines. Prove triangle AEF is also isosceles.

## The bigger picture

In a small square two perpendicular lines are drawn. A larger parallel square is constructed as shown. Prove it is a scaled copy of the smaller square but rotated 90° anticlockwise.

## The Bermuda Triangle

A triangle with an inscribed rectangle. What is the maximum red fraction?