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

# Tag: angle

## Distant Alp II

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

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.)

## 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?

## Spotlight II

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

## Secured package

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

## 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.

## 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?

## The leaning diamond

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

## 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?