The diagram shows two concentric circles. The chord of the large circle is a tangent to the small circle and has length 2k. What is the area of the shaded region?

(a): Put perpendicular from centre to the tangent, it will bisect the chord. Then, by Pythagoras theorem $=$R$2$−$r$2$=$k$2$ $\therefore$ Area of shaded region $=\pi$R$2$−π$r$2=π($R$2$-$r$2$)=π$k$2$Remarks:Thisisaveryg\infty dquestion\to testthe\int elli\ge nceofstudents.O\ne has\to \ne ithercalc\underline{a}teradiusoflar\ge r\circ \le ?R?\text{or}radiusofsmal\le r\circ \le ,?r?.$($R$2$-$r$2$)$issufficientaswe\ne ed\to f\in dn$π($R$2$-$r$2$)\displaystyle{o}{n}{l}{y}.