What-is-the-area-of-overlapping-region-of-two-circles-having-radii-r-1-and-r-2-when-the-distance-between-their-centres-is-c-given-that-r-1-r-2-gt-c- Tinku Tara June 3, 2023 Geometry 0 Comments FacebookTweetPin Question Number 3877 by Rasheed Soomro last updated on 23/Dec/15 Whatistheareaofoverlappingregionoftwocircleshavingradiir1andr2whenthedistancebetweentheircentresisc,giventhatr1+r2>c. Commented by prakash jain last updated on 24/Dec/15 Iwillmakethecorrection.Theaboveprocedureisforcentersondifferentsideofcommonchord. Commented by prakash jain last updated on 24/Dec/15 CommonchordABcenterO1andO2O1O2cutsABatX∠AO1X=α∠AO2X=βAB=2r1sinα=2r2sinβO1X=r1cosα,XO2=r2cosβr1cosα+r2cosβ=careaof△AO1B=12AB×O1X=r12cosαsinαareaof△AO2B=12AB×O2X=r22cosβsinβareaofoverlapinportion=areaofcirclesegment−areaoftriangleAreaofoverlappingportiononsideofcirclewithradiusr1=αr1−area△AO1BX=12αr12−12r12sin2α…(1)Areaofoverlappingportiononsideofcirclewithradiusr2=βr2−area△AO2BY=12βr22−12r22sin2β…(2)Nextstepistofindα,βr1cosα+r2cosβ=c⇒r12cos2α=c2−2cr2cosβ+r22cos2βr1sinα=r2sinβ⇒r12cos2α=r12−r22+r22cos2βc2−2cr2cosβ+r22cos2β=r12−r22+r22cos2βcosβ=c2−r12+r222cr2…(3)cosα=c2−r22+r122cr2…(4)TotaloverlappingareaisX+Yasgiveninequation(1)and(2).valueofαandβgivenin(3)and(4). Commented by Yozzii last updated on 23/Dec/15 Isn′ttheareaofasectorofacircleofradiusrproducedbyangleαgivenby12r2α?rαgivesarclengthno?Isthemethoddifferentifbothcentresareonthesamesideofthecommomchord? Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: x-gt-y-y-2-gt-x-2-Does-such-a-pairing-exist-How-can-you-prove-it-Next Next post: Question-69412 Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.