Question Number 35422 by ajfour last updated on 18/May/18
Commented by ajfour last updated on 19/May/18
$${Sphere}\:{of}\:{radius}\:{R}\:{touches} \\ $$$${plane}\:{at}\:{B}.\:{Line}\:{APQ}\:{intersects} \\ $$$${sphere}\:{at}\:{P}\:{and}\:{Q}.\: \\ $$$${minimum}\:{angle}\:{that}\:{line}\:{makes} \\ $$$${with}\:{plane}\:{is}\:\theta.\:{From}\:{this}\: \\ $$$${minimum}\:{angle}\:{direction}\:{line} \\ $$$${AB}\:{along}\:{plane}\:{makes}\:{an}\:{angle}\:\phi. \\ $$$${AB}=\:{a}\:.\:{Find}\:{length}\:{PQ}\:{in}\:{terms} \\ $$$${of}\:\theta,\phi,{a},\:{and}\:{R}. \\ $$
Commented by ajfour last updated on 19/May/18
$${See}\:{Q}.\mathrm{35430}\:{for}\:{solution}. \\ $$