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.
Two triangles and an extended side. What’s blue : orange?
A square with a diagonal and two circles. What is the area proportion of the two circles?
A circle with an inscribed quadrilateral. Prove that ab=cd.
A circle with two tangents. What’s red : blue in terms of α?
Two squares and an equilateral triangle. Prove that the area of the triangle plus the small square equals that of the large square.
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?
Two overlapping squares and a unit circle. What’s the green overlap area?