Two intersecting circles. Express the lengths b and the common tangent d in terms of c (the distance between the centres) and the angles β and γ.

# Category: Beginner

## Fair scoop

What is the ratio of areas purple : orange if the cone angle is 45°, and the circular arc is a semicircle?

## Square offspring

Three squares and two line segments. What’s the angle α?

## Triangle offspring

Four equilateral triangles. Prove that the three black line segments are concurrent.

## The punctured hexagon

A regular hexagon, a square and an equilateral triangle. Show that the top vertex of the triangle is on the hexagon circumcircle.

## Two-story A-frame house

The slanted lines are perpendicular, and the one in the bottom story bisects the angle. Show that red equals green, so the stories have the same height.

## Angle versus height

What is the ratio orange/green?

## The Bedouin tent

A semicircle and a triangle of which one side is tangent to the semicircle. What is the angle α?

A red equilateral triangle and its circumcircle. Prove that the blue triangle is also equilateral.

## Domino day II

Two large congruent rectangles share a vertex and contain two coloured rectangles. What is red : blue?