please answer the question as soon as possible: in the given figure shown a sector OAP of circle with centre O, containing angle theta . AB is perpendicular to radius OA and meets OP produced at B. prove that the perimeter of the shaded region is :
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tan thetha = AB/OA
AB = OA tan thetha = r tan thetha
cos thetha = r/OB
OB = r/ cos thetha = r sec thetha
therefore BP = r sec thetha - r
PA = pie. r. thetha/180
therefore required perimeter = r tan thetha + pie. r. thetha/180 + r sec thetha -r = r( r tan thetha = pie. r. thetha/180 = sec thetha - 1)
proved.
AB = OA tan thetha = r tan thetha
cos thetha = r/OB
OB = r/ cos thetha = r sec thetha
therefore BP = r sec thetha - r
PA = pie. r. thetha/180
therefore required perimeter = r tan thetha + pie. r. thetha/180 + r sec thetha -r = r( r tan thetha = pie. r. thetha/180 = sec thetha - 1)
proved.
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