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Advanced

Ends of the spectrum

Two squares and a rectangle. Prove that red = blue.

Categories
Intermediate

Square mouse

A semicircle and a square with extended side and diagonal. Prove that the red line segment is tangent to the semicircle.

Categories
Beginner

Triangulation

A regular dodecagon contains a yellow square. Find the three angles α, β and γ.

Categories
Beginner

Paranoid centroid

A square is divided in four triangles of which the red centroids are shown. What fraction is green?

Categories
Intermediate

Blocking the view

Two squares and one extended side. What is purple : red?

Categories
Advanced

Tweezers

A square with two semicircles. The smaller one has an extended diameter and a tangent. What are the coordinates of the tangency point?

Categories
Beginner

Squaring the quad

Form inward semicircles (orange) and outward semicircles (purple) on two opposite sides of a quadrilateral. Connect the midpoints of the orange arcs, intersecting with the purple arcs. Show that you obtain two corners of an enclosing square.

Categories
Advanced

Wheel in motion

A circle with its centre and two squares sharing a vertex. What’s the angle α?

Categories
Beginner

Square construction

Given the blue square AEFI and a point B inside, show that the intersection H of the red and purple semicircles will be a corner of a square containing B on one side and A on another, and sharing the corner I with the blue square.

Categories
Advanced

Distant Alp II

A square with its diagonal. Prove that the three red points are collinear.