Two nested right triangles with their incircles. Two tangency points are shown. Prove that the red and yellow line segments are parallel.
Tag: triangle
Sticky corners
Two equilateral triangles and several line segments. What is red : yellow?
Median between sides
A triangle has sides a,b,c and the medians d,e,f ending at those sides, respectively. Given the lengths (a,b,f) construct the triangle. (Start with a triangle with side lengths determined in some manor from the given 3 lengths.)
The punctured hexagon
A regular hexagon, a square and an equilateral triangle. Show that the top vertex of the triangle is on the hexagon circumcircle.
Circle triplet
Identical circles have their centers aligned as shown, with the middle circle inscribed in a triangle. Show that the outer circles can be made tangent to the green circumcircle if the red axis is rotated correctly.
Wedge the wedge
An equilateral triangle containing an isosceles triangle that is not equilateral. What’s the angle α?
Vanishing point II
Six squares and four coloured triangles. What is red : blue : yellow : green?
Two-story A-frame house
The slanted lines are perpendicular, and the one in the bottom story bisects the angle. Show that red equals green, so the stories have the same height.
Colour convergence
A green line connects two points of tangency of a triangle to its incircle. A red line is the angle bisector at a vertex, and an orange line connects the midpoints of two sides. Show that the three lines are concurrent.
In and out
An obtuse triangle, of which α is the obtuse angle, with its incircle, two cevians and two tangents. Find a relation between α and β.