Let A be an abelian variety defined over a number field K and p be a prime. Define ${varphi}_i=(x^{p^i}-1)/(x^{p^{i-1}}-1)$. Let $A_{{varphi}i}$ be the abelian variety defined over K associated to the polynomial ${varphi}i$ and let Ш($A_{{varphi}i}$) denote the Tate-Shafarevich groups of $A_{{varphi}i}$ over K. In this paper assuming Ш(A/F) is finite, we compute [Ш($A_{{varphi}1}$)][Ш($A_{{varphi}2}$)]/[Ш($A_{{varphi}1{varphi}2}$)] in terms of K-rational points of $A_{{varphi}i}$, $A_{{varphi}1{varphi}2}$ and their dual varieties, where [X] is the order of a finite abelian group X.