Question 25
In the diagram, six touching circles have centres $A,B,C,D,E,F$. The hexagon $ABCDEF$ is regular and $AB=4$. Each side of triangle $PQR$ touches three of the circles. Find the square of the length of $PQ$.
Interpretation: Use the depicted configuration: all circles lie inside the triangle, consecutive circles around the hexagon are externally tangent, and each triangle side is a common supporting tangent to the three circles it touches.
Answer format: an integer without units. Leading zeros are optional; the source uses four digit boxes.
Interpretation: Use the depicted configuration: all circles lie inside the triangle, consecutive circles around the hexagon are externally tangent, and each triangle side is a common supporting tangent to the three circles it touches.
Answer format: an integer without units. Leading zeros are optional; the source uses four digit boxes.