Two equilateral triangles and several line segments. What is red : yellow?
Tag: length
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.)
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.
Angle versus height
What is the ratio orange/green?
Two quarter-circles fit inside a square, and five circles fit inside the overlapped region, centred. What is the ratio of the (straight line) segment lengths red to blue? (The segments connect to points of tangency.)
Ball of yarn
A cyclic hexagon has concurrent cross diagonals. What is the ratio of the product of the orange sides compared to the product of the purple sides. (ace:bdf).
Seeing double II
A right triangle is divided in two triangles by an altitude. The three incircles are shown with three tangency points. Prove that the two red line segments are congruent.
The bike chain II
Two circles and four coloured common tangents. Prove they are congruent.
The mid-circle
A blue right triangle has an orange-dotted circumcircle and a green incircle of radius 7. What is the radius of the purple circle, which is internally tangent to the orange circle and to the two sides of the right angle?
The open roof
A regular hexagon with two line segments at right angles. What is the minimum of yellow : red?