Categories
Intermediate

Caught in the middle

Two circles support a triangle. Prove it is equilateral.

Categories
Intermediate

The magic mirror

You are standing in front of a mirror. Your shoulder width is 50 cm and your eyes are 6 cm apart. What is the minimum mirror width for a stereo view of yourself?

Categories
Intermediate

Daft Mouse

A square with two attached regular pentagons. A side and a diagonal are extended. What’s the angle?

Categories
Intermediate

The colour of spring

A square with a diagonal and a right angle. Two areas are given. How large is the pink area?

Categories
Beginner

The monk’s hood

Two similar triangles inside a semicircle. What’s the angle?

Categories
Intermediate

Mars rover has landed

Two semicircles and two right triangles. What fraction of the large triangle does the small one cover?

Categories
Intermediate

Two hefty volumes

Two congruent rectangles inscribed in a square. What fraction of the area is blue?

Categories
Intermediate

Ménage à trois

Three equilateral triangles of which two are congruent. Are the three points collinear?

Categories
Advanced

The flying banner

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

Categories
Intermediate

Mini and Maxi

Two squares of area 1 and 4 are inscribed in their own triangle and placed as shown. What fraction is coloured?