Categories
Intermediate

Sticky corners

Two equilateral triangles and several line segments. What is red : yellow?

Categories
Intermediate

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.)

Categories
Beginner

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.

Categories
Beginner

Angle versus height

What is the ratio orange/green?

Categories
Advanced

Alien eye

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.)

Categories
Intermediate

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).

Categories
Advanced

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.

Categories
Intermediate

The bike chain II

Two circles and four coloured common tangents. Prove they are congruent.

Categories
Intermediate

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?

Categories
Advanced

The open roof

A regular hexagon with two line segments at right angles. What is the minimum of yellow : red?