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.
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Along similar lines
Category: Advanced
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The hawfinch II
A circle with two tangents. What’s red : blue in terms of α?
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The weather balloon
A circle with three red tangents. The tangency points are marked red. Prove that the yellow triangle is isosceles.
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Count to five
A triangle with a cevian. What’s α?
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The orange pennant
A regular pentagon with two coloured triangles. What’s the proportion orange : blue?
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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.
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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?
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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?
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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?
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Çetins circle
A square, a semicircle and six line segments. What’s the angle α?