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## Silent circle

A large triangle with one side tangent to a circle. The tangency point is the vertex of a blue parallelogram. What is the red area?

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## The yardstick

A rectangle containing a circle and a line segment connecting the top side to the bottom tangency point. What is its area in terms of lengths a and b?

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A semicircle and an inscribed circle. Prove that the circle centre is on the parabola.

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## The Suresh similarity

Two squares and a rectangle. Prove that the red triangles are similar.

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## Tension control

Three squares and a line segment of which a vertex is the midpoint. What is the proportion purple : green?

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## A new slant

Two squares and a slanted rectangle share three vertices. What is the total area?

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## Twin balls

A semicircle with two inscribed circles tangent to an altitude. What’s the angle α?

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## The helmet

A circle, a semicircle, a chord and an altitude. What is the length of the latter in terms of a and b?

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