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.

# Tag: angle

## 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.

## 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.

## 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.

## Falling in

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?

## Smugglers

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?