Question

A carom board $(4cm\times 4cm)$ has the queen at the centre. When the queen is hit by the striker, it moves to the front edge, rebounds and goes into the hole behind the striking line. The displacement of the queen is .

• A. $\frac{2\sqrt{10}}{3}$cm
• B. $20\sqrt{2}cm$
• C. 20cm
• D. $40\sqrt{2}cm$

Answer 1

Answer: (A)

$\frac{2\sqrt{10}}{3}$cm

$△BEC\cong △DFC$ by ASA property.

So,$CF=EC$ by CPCT

and $AE=EC$ by reflection property

$\therefore AE=EC=CF=\frac{2}{3}$

So, ${AB}^2={AE}^2+{BE}^2$

${\left(\frac{2}{3}\right)}^2+2^2=\frac{4}{9}+4=\frac{40}{9}$

$\therefore$ Displacement $AB=\sqrt{\frac{40}{9}}=\sqrt{\frac{4\times 10}{9}}=\frac{2\sqrt{10}}{3}$ cm