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Launch the ball

Express the circle area in terms of the isosceles triangle area A and its side length a.

Author: Marshall W. Buck

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Beginner

Bond of union

Two intersecting circles with two inscribed triangles and two line segments through an intersection point. Prove that the triangles are similar.

Co-author: Marshall W. Buck.

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Beginner

A tight squeeze

Two intersecting circles inside a rectangle and a line segment connecting vertex, intersection point and tangency point. What’s the angle α?

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Zigzag

An equilateral triangle and three line segments. What’s the angle α?

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Beginner

The douche cabine

A square containing three smaller squares and a quarter circle. What fraction is orange?

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Beginner

The quarter trampoline

A quarter circle with two chords of given length. What is the area of the orange quadrilateral?

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Outside the hive

A regular hexagon and two squares. What’s the angle α?

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Egg basket II

What fraction of the regular hexagon is yellow?

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Beginner

Draw the line

A square and an equilateral triangle inside a right triangle. Prove that the three red vertices are collinear.

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Beginner

Another angle

Three congruent squares share three vertices. What’s the angle α?