Correlation — geometric vs. arithmetic mean of the regression coefficients

Consider the following two statements: (1) The correlation coefficient between X and Y is the geometric mean of the two regression coefficients $\beta_{YX}$ and $\beta_{XY}$. (2) The arithmetic mean of the two regression coefficients $\beta_{YX}$ and $\beta_{XY}$ is greater than or equal to the correlation coefficient between X and Y.