Let $T_1$ be a circle with centre at the point $O$ and radius $R$. Two other circles $T_2$ and $T_3$ with centres at $O_2$ and $O_3$ respectively are tangent internally to $T_1$ and meet each other ($T_2$ and $T_3$) at the points $A$ and $B$. Find the sum of the radii of $T_2$ and $T_3$. $R_2$ + $R_3$, if $\angle OAB = \pi/2$.
[OP's thoughts, added by Brian Tung] I got $O_2AO_3B$ is a Kite. Also if extend $OA$ and intersects $T_3$ to point $W$ in $T_2$ for example, and extend $AO$ to $T_2$ then intersect $T_2$ to $V$, can get $O_2O_3$ equal to half of $WV$. If I can approve $WV$ is paralleling to $O_2O_3$ or $OO_3$ is paralleling to $WB$, may get the result of $R_2 + R_3 = R$. Not sure if this is the right direction?
