Some chords and segments inside a semicircle. What is the ratio of red to blue?
Month: August 2023
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Three times three
A regular nonagon and two equilateral triangles. What’s the angle α?
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The laser game
In an equilateral triangular mirror room a laser is shot from the top vertex down to the base. The light ray bounces three times to return to the same base point. What is the angle α?
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Three dome home
How does the white area inside the big semicircle compare to the combined white areas of the 3 smaller semicircles below it? Equally coloured semicircles are congruent.
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The hex division
A regular hexagon with two diagonals and two perpendiculars. What’s red : yellow?
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The basketball court
An orange circle is squeezed inside a rectangle. Show that no matter how the blue point moves on the circle, the derived points Q and P will satisfy |QL| = |KP|.
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The owl of Ceva
A triangle with three concurring cevians. What’s orange : blue?
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Circle sandwich
The red and green child-circles squeeze their father (the blue circle) in the back seat while their mother drives. Show that the orange points where the children sit and where the children are squeezing their father are concyclic.
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In the red
Two congruent semicircles with their centres and a chord. Prove that the two red triangles are congruent as well.
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The vanilla ice cream
A regular pentagon with two extended sides and a right angle. What is blue : green?