1956 AMC 12 Question 38
AMC12 · 1956 AMC 12
In a right triangle with sides $a$ and $b,$ and hypotenuse $c,$ the altitude drawn on the hypotenuse is $x.$ Then:
$ab=x^2$
$\dfrac1a+\dfrac1b=\dfrac1x$
$a^2+b^2=2x^2$
$\dfrac1{x^2}=\dfrac1{a^2}+\dfrac1{b^2}$
$\dfrac1x=\dfrac ba$