As shown in the figure, let the triangle surrounded by three highways be △ABC, and the intersection points of bisectors of inner and outer angles are O, O 1, O2, O3, where OD⊥AC is in D, OE⊥BC is in E, and OF⊥AB is in F.

∫AO shares ∠BAC, CO shares ∠ACB,

∴OD=OF,OD=OE，

∴OD=OE=OF，

That is, the distance from point O to each side of the triangle is equal;

Similarly, it can be proved that the distances from points O 1, O2 and O3 to each side of the triangle are equal.