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
Two-story A-frame house
Tag: angle
Categories
Balancing act II
Two squares share a vertex. What’s the angle α?
Categories
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
Angle versus height
What is the ratio orange/green?
Categories
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
The Bedouin tent
A semicircle and a triangle of which one side is tangent to the semicircle. What is the angle α?
Categories
Six four
A regular hexagon and an inscribed tilted rectangle. What is the angle α?
Categories
The silly walk
A circle and several triangles. Prove that the green triangle is isosceles.
Categories
The sun hat
Two triangles share a circumcircle and vertex, with one edge of the orange triangle containing the feet of two of the altitudes of the blue triangle. Show that the orange triangle is isosceles.
Categories
Uneasy the head
The green zigzag crown segments would extend through either B or C. Show that the arcs along the top are equally spaced.