The vertices of an equilateral triangle are connected to an interior point. What is the angle α?
Tag: triangle
Darth Vader
A regular hexagon containing three diagonals and three congruent circular arcs. What fraction is black?
Sisyphus
A semicircle containing two circles and two triangles. The blue right triangle connects three tangency points. Prove it is isosceles.
The triangle trio
Three triangles, one of which is right and one is isosceles, form a large triangle. Two side lengths are given. What fraction of the total area is red?
The two jabs
Two congruent equilateral triangles share a vertex. What is the angle α?
The single parent holiday
An equilateral triangle containing two circles of given area and a common tangent divided in two. What is the proportion of the two parts?
The birdwatcher
Two congruent circles and a right triangle inside a semicircle. What fraction is blue?
The tin foil hat
A circle inside a quarter circle. The triangle connects the two tangency points and the top of the quarter circle. What’s the angle α?
The hammock
A square inscribed in a triangle. Two areas are given. What is the square’s area?
The twin triangles
Two squares share a vertex. Prove that the red triangle is congruent to the blue one.