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.
The hawfinch II
A circle with two tangents. What’s red : blue in terms of α?
The weather balloon
A circle with three red tangents. The tangency points are marked red. Prove that the yellow triangle is isosceles.
Count to five
A triangle with a cevian. What’s α?
The orange pennant
A regular pentagon with two coloured triangles. What’s the proportion orange : blue?
On a tangent
Two tangent circles and their three common tangents. Two secants meet on the internal tangent. Prove that the three red points are collinear.
The new normal
Two equilateral triangles are placed as shown. Their centres are connected as well as their intersection points. What’s the angle α?
The Moroni minimum
An arbitrary point on the parabola y=x2. Shown are the tangent in that point and a line segment perpendicular to it. What is the minimal height h?
The common ground
Two squares share a vertex. Two other vertices are 4 units apart. A third green square has the centres as opposite vertices. What is its area?
A square, a semicircle and six line segments. What’s the angle α?