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.
What is the ratio orange/green?
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.
A semicircle and a triangle of which one side is tangent to the semicircle. What is the angle α?
A regular hexagon and an inscribed tilted rectangle. What is the angle α?
A circle and several triangles. Prove that the green triangle is isosceles.
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.
The green zigzag crown segments would extend through either B or C. Show that the arcs along the top are equally spaced.
Start with an acute triangle and form a new triangle from the points of tangency of its inscribed circle. Continue this process to make make the triangle with blue vertices. What is the maximum possible angle at a blue vertex?
The smugglers want to land half-way between the lighthouses. It is a dark night, so they keep their boat heading at an angle bisecting the angle to the two lights. Where on the shore should the coast guard wait to intercept them?