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Advanced

Wheel in motion

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

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Advanced

Distant Alp II

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

Categories
Beginner

Bullseye

Blue and orange concentric circles intersect a vertical line in green dots. Show that the dots are equally spaced, given that the red intervals shown are of equal length. (The largest circle has radius 2u.)

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Advanced

Equilateral linkage

Given 3 points A, B, C, define G so CG=CB and angle GCB is 120 degrees. Define M as the midpoint of side CH of the parallelogram CGAH. The green equilateral has side CM and the purple equilateral has side MB. Is AJK also equilateral?

Categories
Intermediate

Spotlight II

A square is divided in several triangles and quadrilaterals. What is yellow : red?

Categories
Intermediate

Secured package

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

Categories
Intermediate

The drinking bird

Two circles with two radii and two tangents. The blue line passes through points of tangency and the circle intersection. Prove that α=β.

Puzzle author: David Odell.

Categories
Intermediate

Circle crossings

The segment CD is tangent to the green circle c, ending on the orange circle d, which also contains the foot of the perpendicular line from C to the diameter of c which extends to D. What is the angle between the two circles?

Categories
Beginner

The leaning diamond

A square with two equilateral triangles. What’s the angle α?

Categories
Intermediate

The dunce cap

The orthocentre H, circumcentre O, the incentre I, and points B and C all lie on the top of the dunce’s spherical head. What is the angle α?