Categories
Intermediate

The triangle trio

Three triangles, one of which is right and one is isosceles, form a large triangle. Two side lengths are given. What fraction of the total area is red?

Categories
Intermediate

The single parent holiday

An equilateral triangle containing two circles of given area and a common tangent divided in two. What is the proportion of the two parts?

Categories
Intermediate

The tin foil hat

A circle inside a quarter circle. The triangle connects the two tangency points and the top of the quarter circle. What’s the angle α?

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Intermediate

Lazy Friday

Four congruent squares plus another one. What is the angle α?

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Intermediate

The fez

A circle and a semicircle inside a square. What’s the length proportion of the two chords?

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Intermediate

The cleaver

Four squares, a rectangle and a circle. What is the proportion brown : grey?

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Intermediate

The twin triangles

Two squares share a vertex. Prove that the red triangle is congruent to the blue one.

Categories
Intermediate

Ice cube

A rectangle and a square. What is the proportion purple : blue?

Categories
Intermediate

The hourglass

A rectangle with two crossing line segments. What’s the minimal shaded fraction?

Categories
Intermediate

Below the tree line

A triangle is split in two. What is the area of the green quadrilateral in terms of lengths a and b?