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.
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.
A circle with two tangents. What’s red : blue in terms of α?
A circle with three red tangents. The tangency points are marked red. Prove that the yellow triangle is isosceles.
A triangle with a cevian. What’s α?
A regular pentagon with two coloured triangles. What’s the proportion orange : blue?
Two tangent circles and their three common tangents. Two secants meet on the internal tangent. Prove that the three red points are collinear.
Two equilateral triangles are placed as shown. Their centres are connected as well as their intersection points. What’s the angle α?
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?
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?