Categories
Intermediate

The doubleganger

Two nested right triangles with their incircles. Two tangency points are shown. Prove that the red and yellow line segments are parallel.

Categories
Intermediate

Wedge the wedge

An equilateral triangle containing an isosceles triangle that is not equilateral. What’s the angle α?

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
Intermediate

Balancing act II

Two squares share a vertex. What’s the angle α?

Categories
Intermediate

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.

Categories
Beginner

Angle versus height

What is the ratio orange/green?

Categories
Intermediate

Wheel of fortune II

A triangle with its incircle and three cevians. The tangency points and incentre are shown. Find the relation between the angles α, β and γ.

Categories
Beginner

The Bedouin tent

A semicircle and a triangle of which one side is tangent to the semicircle. What is the angle α?

Categories
Intermediate

Six four

A regular hexagon and an inscribed tilted rectangle. What is the angle α?

Categories
Intermediate

The silly walk

A circle and several triangles. Prove that the green triangle is isosceles.