We have $ \frac {\overline{A_iQ_i}}{\overline{Q_iA_{i + 2}}} = \frac {\bigtriangleup A_iPA_{i + 1}}{\bigtriangleup A_{i + 2}PA_{i + 1}},i = 1,2,3,4,5$ Mutiply all these five equations and we can get $ \prod_{i = 1}^{5}\frac {\overline{A_iQ_i}}{\overline{Q_iA_{i + 2}}} = 1$ ..........(i) However, suppose $ \overrightarrow{A_iO}$ meets the circle at $ {A}'_i$, then the circle power of $ Q_i = \overline{A_{i + 1}Q_i}\cdot\overline{Q_i{A}'_{i + 1}} = (1 + d_{i + 1})(1 - d_{i + 1}) = \overline{A_iQ_i}\cdot\overline{Q_iA_{i + 2}}$ That is ${ \overline{A_iQ_i}\cdot\overline{Q_iA_{i + 2}} = (1 - d_i^2}),i = 1,2,3,4,5$ Mutiply all these five equations and we can get ${ \prod_{i = 1}^{5}\overline{A_iQ_i}\cdot\overline{Q_iA_{i + 2}} = (1 - d_i^2})$ .........(ii) $ \sqrt {(i)\times (ii)}\Rightarrow \prod_{i = 1}^{5}{\overline{A_iQ_i}} = \prod_{i = 1}^{5}\sqrt{(1 - d_i^2)}$ QED#