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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Silent circle
Month: April 2022
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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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The Arcus arcade
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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Equilibrium
Three squares and a circle. The areas of the squares are given. What is the area of the circle?
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The pyramid scheme
Two congruent circles and a triangle. Prove that the triangle is isosceles.