Show that the green dotted line, which is an altitude of the blue triangle, is also a median of the orange triangle.
Categories
Highway confusion
Month: December 2023
Categories
The brick oven
Five congruent rectangles. What’s their proportion width : height (aspect ratio)?
Categories
Inside the box II
A square contains four other squares. Prove that the red line segment is parallel to its vertical sides.
Categories
Decorating the tree
A symmetric tree has decorative lines of equal slope, and of lengths 11 and 13. What is the area ratio of green to red to brown?
Categories
The brick pile
Three congruent rectangles inscribed in a triangle. What fraction is brown?
Categories
The mis-stacked trays
A rectangle is turned 90°, bisecting a bigger rectangle of the same shape. When squares are removed from the two side pieces, the remaining rectangles have the same shape as well. What is the common ratio of the rectangle side lengths?
Categories
Compartmentalization
A square with two circles and two common tangents. What’s red : blue?
Categories
Scratching the surface II
Two equilateral triangles, the smaller one being of variable size. What is the minimum value of orange : blue?
Categories
Land and sea
Two circles, some triangles, and a blue tangent line to the orange circle. Show that the two green triangles are similar.
Categories
Inside the box
Two squares inside a square share a vertex. What’s the angle α?