Categories
Intermediate

The japanese progression

An isosceles trapezium with its inscribed circle. If the lengths are such that b-a=c-b=d-c, what is a : b : c : d?

Categories
Intermediate

The bear trap

A semicircle with two tangents and a perpendicular line segment from a tangency point. What is the blue area in terms of lengths a and b?

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Beginner

The road less traveled

What is the area of the trapezium in terms of lengths a and b?

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Intermediate

The hand fan

Three congruent triangles constitute a quadrilateral. What’s red : blue?

Categories
Intermediate

The triple airbag

A triangle containing three tangent semicircles with diameters a, b and c. Three line segments pass through the red tangency points. What is the triangle perimeter?

Categories
Intermediate

At navel level

Two equilateral triangles share a vertex. The centre of the larger one is aligned with the midpoint of a side of the smaller one. What is green : red?

Categories
Intermediate

The common focus

A parabola, its symmetry axis and a tangent. Yellow connects the focus to the intersection point. Red connects the focus to the tangency point. What’s yellow : red?

Categories
Beginner

The purple hat

A circle with three tangents forming an isosceles triangle. Two tangency points are shown. What is the proportion green : red?

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Intermediate

Two hemispheres

A triangle with its circumscribed circle and a smaller intersecting circle. The two intersection points and the circumcentre are shown. What’s the proportion red : green?

Categories
Intermediate

The wedge

A trapezium with its inscribed circle. Two tangency points are shown. What’s red / blue – yellow / green?