A square of variable size inscribed in a semicircle of radius r. What is the maximum distance d of the lowest square vertex to the nearest semicircle corner?
Categories
The sliding square
Tag: maximum
Categories
The turning point
Two isosceles triangles share a vertex. What is the maximum of their area proportion red/green?
Categories
Mind the gap
A regular hexagon with an equilateral triangle sharing a vertex and having a vertex somewhere along the opposite side. What is the maximum length of line segment g?
Categories
The Queen’s chamber
A right triangle with three squares forming a smaller inner triangle. What is the maximal blue fraction?
Categories
The ocean view
Two squares of variable size share a vertex. What is the maximal blue fraction?
Categories
The Bermuda Triangle
A triangle with an inscribed rectangle. What is the maximum red fraction?
Categories
The rolling stones
If you roll a circle down a parabola, small circles can roll all the way down and up, whereas large circles get stuck between the sides at some point. What is the transition radius? In other words, what’s the maximum circle that keeps on rolling?
Categories
The PowerPoint
A point lies 8 from the centre of a circle of radius 6. The angle α is variable. What’s the maximum triangle area?
Categories
Don Quixote and the windmill
Don Quixote is approaching a windmill. The sails of length √2 are attached to a point that is 2 above eye level. What is the maximum vertical angle that Don Quixote perceives as he moves forward?
Categories
Beware of the dots
Two congruent circles and a common tangent. A triangle connecting tangency points and the upper intersection point. What angle α maximises its area?