Categories
Intermediate

The hemispheric battle

C fires at city B and D fires at city A, but their rockets collide in mid-air and fall into the ground at F. Then C fires a laser bouncing off the ground at F at the same angle as incidence. Will the laser beam hit combatant D?

Categories
Beginner

A tight squeeze

Two intersecting circles inside a rectangle and a line segment connecting vertex, intersection point and tangency point. What’s the angle α?

Categories
Beginner

Zigzag

An equilateral triangle and three line segments. What’s the angle α?

Categories
Intermediate

To the max

Two squares and two line segments. If the angle α is maximal, what is yellow : red?

Categories
Beginner

Outside the hive

A regular hexagon and two squares. What’s the angle α?

Categories
Intermediate

A fair division II

Two squares sharing a vertex, a diagonal and a line segment. Prove that the two angles are congruent.

Categories
Beginner

Another angle

Three congruent squares share three vertices. What’s the angle α?

Categories
Intermediate

The bike chain

A square containing a semicircle, a circle and two tangents. What’s the angle α?

Categories
Advanced

Fireworks

A triangle and two semicircles. What’s the angle α?

Categories
Intermediate

North by Northwest

An equilateral triangle and a rectangle. What’s the angle α?