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?

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?

Answer: Option A

Solution

Answer: Option A

Solution:

$$\begin{array}{rl}& R{T}^2=25^2-20^2\\ & RT=15\\ & \text{Inradius }\left(\text{r}\right)=\frac{20+15-25}{2}=\frac{10}{2}=5\\ & \text{In }\Delta O_{1}A{O}_2\\ & O_1{O}_2^2=O_1{A}^2+A{O}_2^2\\ & ={\left(5\right)}^2+{\left(15\right)}^2\\ & =25+225\\ & =250\\ & O_1{O}_2=5\sqrt{10}\text{ cm}\end{array}$$