An equilateral triangle containing a parallelogram, another equilateral triangle and a circular arc that is tangent in its base vertices. What is the proportion pink : blue?
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Out of proportion
Category: Advanced
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Circular architecture
An equilateral triangle and two circles. The centre of the right circle is the triangle side midpoint. Both circle intersections lie on a triangle side. Prove that the three red circular arcs are congruent.
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Out of focus
A semicircle with an inscribed triangle. Both circles are tangent to the semicircle, the diameter and one other triangle side. Prove that the line segment connecting the two shown tangency points is parallel to the diameter.
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The sacrosanct circles
Two tangent circles and two tangent line segments meeting in a point on the outer circle. The tangency points are connected by a line segment of length x. What’s x in terms of a and b?
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Extreme parallelism
Four parallel line segments, one of which is divided in three parts. What is the proportion blue : red : green?
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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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Twin balls
A semicircle with two inscribed circles tangent to an altitude. What’s the angle α?
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The square of Amaresh
A right triangle having semicircles along its perpendicular sides and two smaller inscribed circles. Prove that the orange quadrilateral is a square.
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Stuck in the middle
A right triangle with semicircles along its perpendicular sides having lengths a and b. Two smaller inscribed circles. What is the proportion blue : red in terms of a and b?
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Eye of the apple
A circle with an inscribed triangle with an inscribed circle. The centre of the large circle is on the small one. What fraction of the area is blue?