Categories
Intermediate

The lorgnette

An ellipse, two circles centred in its focal points, a chord and a tangent. What is the angle α?

Categories
Intermediate

The truss bridge

Two lines connected by five triangles. Prove that orange = blue.

Categories
Intermediate

The sandal

A triangle with two angular bisectors. What’s the proportion blue : red?

Categories
Intermediate

The gate

Two equilateral triangles sharing a vertex and three line segments. Prove that the red triangle is isosceles.

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Intermediate

Meeting halfway

Two squares and three line segments. What’s the angle α?

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Intermediate

A square deal

A regular hexagon and a square share a vertex. What’s the angle α?

Categories
Intermediate

The balloon incident

A circle with a red and a green tangent. The two tangency points are shown. Prove that the blue and red line segments are parallel.

Categories
Intermediate

The pink diamond

Two congruent rectangles inside a square. What fraction of the square is the rectangle overlap?

Categories
Intermediate

The radical

Two intersecting circles and a common tangent. The two tangency points are shown in black. Prove that the three red points are collinear.

Categories
Intermediate

Getting stuck

A regular pentagon and a circle through two of its vertices and its centre. What’s the angle α?