A square with an extended side. What’s the angle α?
Along similar lines
The blue triangle is similar to the green one and has the same orientation. The midpoints between corresponding vertices are connected to form a red triangle. Prove that it is also similar.
Four orange unit circles and their red centres. What is the radius of the green circle? Kindly provided by Marshall W. Buck.
Rule of 72
Two triangles and an extended side. What’s blue : orange?
The bubble chamber II
A square with a diagonal and two circles. What is the area proportion of the two circles?
Sailing by night
A circle with an inscribed quadrilateral. Prove that ab=cd. Kindly provided by Marshall W. Buck.
The hawfinch II
A circle with two tangents. What’s red : blue in terms of α?
Outside the frame
Two squares and an equilateral triangle. Prove that the area of the triangle plus the small square equals that of the large square.
The odd balance
Two circles are tangent to two perpendicular lines and have their centres connected. Prove that the green triangle is right isosceles.
Three squares and three line segments. What’s the angle α?