Two regular hexagons share a vertex. What is the angle α?

# Tag: angle

## Centre stage

A square with its centre and a right angle. What’s ad-bc?

## The fountain plaza

The incircle of ABC touches sides at I and J. D, E, F are the bases of altitudes from C, B, and A. The incenters of BDF of CEF are N and M, respectively. Show that JIMN is a parallelogram and that IM is perpendicular to BC.

## Pentagon offspring II

Two regular pentagons, one of which has an extended side. What’s the angle α?

## Shoulder to shoulder

Two equilateral triangles sharing a vertex and several line segments. What’s the angle α?

## The happy couple

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

## Tipping point II

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

## Drilling site

A blue flagpole is erected near a drilling site. Lines are drilled perpendicular to the flagpole guy wires and meet at the bottom of the orange drilling pipe. What is the ratio of distances green to red?

## Cathedral on the hills

A cathedral is erected on two hills, the side circular arcs whose centers are the hill ends, and so that the right (and left) side arcs are orthogonal. Show that the tip of the spire is directly above where the hills meet.

## Triangulation

A regular dodecagon contains a yellow square. Find the three angles α, β and γ.