Two nested right triangles with their incircles. Two tangency points are shown. Prove that the red and yellow line segments are parallel.
Tag: angle
Wedge the wedge
An equilateral triangle containing an isosceles triangle that is not equilateral. What’s the angle α?
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.
Balancing act II
Two squares share a vertex. What’s the angle α?
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.
Angle versus height
What is the ratio orange/green?
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.
The Bedouin tent
A semicircle and a triangle of which one side is tangent to the semicircle. What is the angle α?
Six four
A regular hexagon and an inscribed tilted rectangle. What is the angle α?
The silly walk
A circle and several triangles. Prove that the green triangle is isosceles.