An equilateral triangle inside a rectangle. What is red : yellow : blue?
Categories
Primary colours
Category: Intermediate
Categories
Mountain roads
A circular mountain peak has coordinates (0,0,3) and its base has towns C=(-4,0,0), E=( 4,0,0) on opposite sides. Town D=(0,4,0) is halfway between them, around the base. A road goes partially up and down the mountain connecting C and E. Another road connects C and D. Both roads are shortest possible. What is the ratio of the road lengths?
Categories
The same vein
Two similar triangles ABC and EBD. Two line segments meet at point F. Prove that ABFC and EBDF are cyclic quadrilaterals.
Categories
The pentagon proportion
A regular pentagon and a circular arc through its red centre. What’s the proportion α : β?
Categories
In touch
A regular nonagon and four equilateral triangles. The purple and yellow triangles share a vertex. Prove that the yellow triangles also share a vertex.
Categories
The party hat II
An equilateral triangle with a circular arc through its red centre and two vertices. If the yellow area equals the green one, what’s the angle α?
Categories
Holes in my heart
The heart is divided into right triangles, each of which contains a blue circle. What is the total circumference of the blue circles in relation to the green perimeter and the lengths of the purple and orange lines in the centre?
Categories
Three times three
A regular nonagon and two equilateral triangles. What’s the angle α?
Categories
The hex division
A regular hexagon with two diagonals and two perpendiculars. What’s red : yellow?
Categories
The owl of Ceva
A triangle with three concurring cevians. What’s orange : blue?