Regression coefficients: $c/a=\sigma_X^2/\sigma_Y^2$, $ac=r^2$, and the lines meet at the means

Let the regression lines of Y on X and X on Y be $Y=aX+b$ and $X=cY+d$ respectively. Consider the statements: (1) The ratio of the variances of X and Y is $c/a$. (2) The correlation coefficient between X and Y is $\sqrt{ac}$. (3) The values of $\bar X$ and $\bar Y$ are $\dfrac{cb+d}{1-ac}$ and $\dfrac{ad+b}{1-ac}$ respectively. Which of the above statements are correct?