Two squares and some line segments. Find the relation between the angles α and β.
Category: Beginner
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Four squares
How does the average of the areas of the blue and green squares compare with the area of the purple square?
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Steam roller
Two intersecting circles. Express the lengths b and the common tangent d in terms of c (the distance between the centres) and the angles β and γ.
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Fair scoop
What is the ratio of areas purple : orange if the cone angle is 45°, and the circular arc is a semicircle?
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Square offspring
Three squares and two line segments. What’s the angle α?
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Triangle offspring
Four equilateral triangles. Prove that the three black line segments are concurrent.
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The punctured hexagon
A regular hexagon, a square and an equilateral triangle. Show that the top vertex of the triangle is on the hexagon circumcircle.
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Angle versus height
What is the ratio orange/green?
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The Bedouin tent
A semicircle and a triangle of which one side is tangent to the semicircle. What is the angle α?