it is very easy if you consider a coordinate system through the diamtere and $(0,0)$ as the center then the divison points will be $A= (-R,0) , B=(-R/2,0) , O=(0,0) , C=(R/2,0) , D=(R,0)$ $P$ be any point on the circle ....so $P= (R \cos(\theta) , R \sin(\theta))$ so ....$AP^2 = (R + R \cos(\theta))^2 + R^2.\sin^2(\theta)$ $BP^2 = (\frac{R}{2} + R \cos(\theta))^2 + R^2.\sin^2(\theta)$ $OP^2 = R^2 \cos^2(\theta)) + R^2.\sin^2(\theta)$ $CP^2 = (\frac{R}{2} - R \cos(\theta))^2 + R^2.\sin^2(\theta)$ $DP^2 = (R + R -cos(\theta))^2 + R^2.\sin^2(\theta)$ so sum will be .....$(2R^2 + 5.\frac{R^2}{2} + R^2 + 5.\frac{R^2}{2} + 2R^2) = \frac{15R^2}{2}$