A triangle with a quadrilateral that covers half its area. What is the angle?

# Category: Advanced

## The PowerPoint

A point lies 8 from the centre of a circle of radius 6. The angle α is variable. What’s the maximum triangle area?

## Who’s afraid of red, yellow and blue?

Three squares. The top line segment is variable in length. What’s the minimal blue fraction?

## Don Quixote and the windmill

Don Quixote is approaching a windmill. The sails of length √2 are attached to a point that is 2 above eye level. What is the maximum vertical angle that Don Quixote perceives as he moves forward?

## Whiskey on the rocks

Two squares share a vertex. An isosceles triangle connects three others. What fraction is blue?

## The complicated jet

Two congruent squares inside a circle. The extended diagonals meet at the circle circumference. What’s their angle?

## The dark side

A quarter circle containing two touching semicircles cut by a chord. What fraction is brown?

## The carambole

Three touching congruent circles inscribed in an equilateral triangle. A small equilateral triangle inscribed in the centre space. What fraction is blue?

## The christmas tree

A triangle, a median and another cevian. What is the proportion of the two areas?

## The tip of the iceberg

A triangle with a 45° angle is placed inside a square as shown. What’s the area proportion of parts A and B?