| dc.description |
Let AB and BC be two circular arcs subtending angles 2α and 2β at the common centre 0. From symmetry the centroids G<sub>1</sub>, G<sub>2</sub> and G of AB, BC and AC lie on the bisectors OP, OQ andOR of the angles which they subtend at the centre. Also, G is the centroid of two particles placed at G<sub>1</sub> and G<sub>2</sub>, and with masses proportional to the arcs AB and BC. Hence G<sub>1</sub>, G, and G<sub>2</sub> are collinear, andEquating (1) and (2) we haveHence the ratio is independent of α, and thereforethe angle α. being in circular measure. |
