Categories
Beginner

The dirty thirties

A triangle containing a semicircle and a circular sector centred in the right vertex. What is blue : green?

Categories
Intermediate

Scratching the surface

Three tangent semicircles and two coloured triangles. What’s the proportion yellow : green?

Categories
Intermediate

To the core

A non-isosceles triangle with a red cevian and three line segments to a point on the cevian. Prove that this point is the incentre of the triangle.

Categories
Intermediate

The seventh bell

A regular hexagon shares a vertex with an equilateral triangle of area 7. What is the area of the hexagon?

Categories
Beginner

Eleven

A square contains a yellow right triangle with an area of 11. What is the square’s area?

Categories
Intermediate

The erratic spider

A square with several line segments. Prove that the blue ones are parallel.

Categories
Beginner

Almost sunk

A square contains a right triangle. What fraction is red?

Categories
Intermediate

The side mirror

An isosceles triangle and an external point with three line segments. Prove that the red points form a cyclic quadrilateral.

Categories
Advanced

The Santos conundrum

A triangle is divided by three line segments into five smaller triangles. What is its area expressed in terms of areas A, B and C?

Categories
Intermediate

Two brotherly pines

Three triangles are glued together. The green ones are based on a common line. What’s the angle α?