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Question-35422




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

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