14. Let $A B C$ be a right triangle at $A$, with $A \widehat{B} C=15^{\circ}$. Let $H$ be the foot of the altitude from $A$ and let $J, K$ be the projections of $H$ onto $A B$ and $A C$. Knowing that the area of $A J H K$ is $45 \mathrm{~cm}^{2}$, how many $\mathrm{cm}^{2}$ is the product $B J \cdot C K$?
14. The answer is 45. Setting \(x = AJ\), \(y = AK\), \(x' = JB\), and \(y' = KC\), we have, using the second theorem of Euclid, \(x \cdot x' = y^2\) and \(y \cdot y' = x^2\). Multiplying member by member, we get \((x \cdot x')(y \cdot y') = (x' \cdot y')(x \cdot y) = x^2 \cdot y^2\), from which \(x' \cdot y' = x \cdot y = 45\).