Three circles and a triangle. What is red : green?
Categories
Siamese triplet III
Month: June 2024
Categories
Common tangents
Two tangent circles and a third circle between the centers. Show that the 3 circles have a common tangent line, and that the middle point of tangency is directly above the point where blue and green touch.
Categories
Siamese triplet II
Three circles with a common intersection and two chords. Prove that the three red points are collinear.
Categories
Turkey weave
Green and blue “turkeys” with feet fixed at points A, B, C, D along the line, have their feathers interleaved. Show that every green-blue pair of circles intersect in points that are collinear with a single fixed point on the ground.
Categories
The Siamese triplet
Three circles with a common intersection point and two triangles. What is α : β?
Categories
Red pistil
Three circular petals surround a red pistil which is orthogonal to each of the petals. Given the petals, construct the pistil. (You may assume that you are given a direct way to construct a tangent line from an exterior point to any circle.)
Categories
Consecutive numbers
A triangle with its incircle. What’s a : b : c?
Categories
Hex division II
A regular hexagon and two equals angles. What is blue : green : red?
Categories
Blocking the view
Two squares and one extended side. What is purple : red?
Categories
Nearly the same
Two rectangles are positioned with the side of each one along the diagonal on the other. Furthermore, two of their sides have the same length, as marked. What is the quotient of areas (A+B)/(C+D)?