In the given figure, PQRS is a square of side 20 cm and SR is extended to point T. If the length of QT is 25 cm, then what is the distance (in cm) between the centers O₁ and O₂ of the two circles?

Solution (By Examveda Team)

$$\eqalign{ & R{T^2} = {25^2} - {20^2} \cr & RT = 15 \cr & {\text{Inradius }}\left( {\text{r}} \right) = \frac{{20 + 15 - 25}}{2} = \frac{{10}}{2} = 5 \cr & {\text{In }}\Delta {O_1}A{O_2} \cr & {O_1}O_2^2 = {O_1}{A^2} + AO_2^2 \cr & = {\left( 5 \right)^2} + {\left( {15} \right)^2} \cr & = 25 + 225 \cr & = 250 \cr & {O_1}{O_2} = 5\sqrt {10} {\text{ cm}} \cr} $$