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Question-59700




Question Number 59700 by ajfour last updated on 13/May/19
Commented by ajfour last updated on 13/May/19
Find maximum overlap of the  quarter circle and semicircle both  of the same radius and in the  shown orientation as a percentage  of the quarter circle area.
$$\mathrm{Find}\:\mathrm{maximum}\:\mathrm{overlap}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{quarter}\:\mathrm{circle}\:\mathrm{and}\:\mathrm{semicircle}\:\mathrm{both} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{same}\:\mathrm{radius}\:\mathrm{and}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{shown}\:\mathrm{orientation}\:\mathrm{as}\:\mathrm{a}\:\mathrm{percentage} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{quarter}\:\mathrm{circle}\:\mathrm{area}. \\ $$
Commented by ajfour last updated on 13/May/19
Commented by ajfour last updated on 13/May/19
for clarity the quarter circle radius  is more than the semi-circle radius.
$$\mathrm{for}\:\mathrm{clarity}\:\mathrm{the}\:\mathrm{quarter}\:\mathrm{circle}\:\mathrm{radius} \\ $$$$\mathrm{is}\:\mathrm{more}\:\mathrm{than}\:\mathrm{the}\:\mathrm{semi}-\mathrm{circle}\:\mathrm{radius}. \\ $$
Commented by ajfour last updated on 14/May/19
MJS Sir, MrW Sir ?
$$\mathrm{MJS}\:\mathrm{Sir},\:\mathrm{MrW}\:\mathrm{Sir}\:? \\ $$
Commented by MJS last updated on 14/May/19
I tried but I couldn′t find a working point
$$\mathrm{I}\:\mathrm{tried}\:\mathrm{but}\:\mathrm{I}\:\mathrm{couldn}'\mathrm{t}\:\mathrm{find}\:\mathrm{a}\:\mathrm{working}\:\mathrm{point} \\ $$

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