A semicircle is inscribed in a rectangle. What is the minimal covered fraction?

# Category: Advanced

## The satellite

A circle containing three squares. What fraction is coloured?

## The eye mask

A right triangle with its inscribed circle. Two cevians are drawn through the circle centre. What is the circle area in terms of triangle areas A and B?

## The green quad

Three semicircles and a circle all touching each other. The diameters of the two smallest semicircles are given. The large triangle connects three tangency points. What is the area of the green quadrilateral?

## Triangle quartet II

Three coloured equilateral triangles share three vertices. Prove that the triangle formed by their centres is also equilateral.

## The lemon slice

A semicircle is inscribed in a quarter circle. What is the minimal yellow fraction?

## The Magdeburg hemispheres

A square containing a circle and two semicircles, all three having the same radius. What fraction is purple?

## The screwball ice cream

A circle of radius r touching both sides of a parabola having focal length a. A line segment tangent to the circle is split in two equal segments of length d. What is d in terms of r and a?

## The tortilla wrap

The edge of a circle is folded to touch a diameter. The tangency point lies 2 from the centre. Given that the fold has length 4, what was the circle area before folding?

## The birdwatcher

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