IIT JEE , AIEEE Forum - Mathematics , Algebra

sreyab

two equal circles of radius 7 cm have their centers 10 cm apart.What is the area common to both circles?

manoj_babu

suppose let the circles meet at two pts P,Q n let the centres be R,S. now RP=RQ=SP=SQ=7=>PQRS is a square

<PRQ=90 area of sector PRQ=77/2 n area of triangle PQR is 1/2.7.7=49/2

area common to both circles =2(77/2-49/2)=28

krishna.gopal

Manoj your answer is wrong. You can't use area of triangle as (1/2)*7*7

Lets take the poits as taken by Manoj. Let PQ intersects RS at T.
In Triangle PRT
PR=7 cn
RT= 5 cm
So PT=sqrt(49-25)=2sqrt(6).
Angle PRQ=2*cosinvers(5/7)=theta
Commomn area = 2*area of sector PQTP
=2*(theta*7*7/2-area of triangle PQR)
=2*(theta*7*7/2-7*2*sqrt(6)/2
=49*theta-14sqrt(6)
where theta is cosinvers(5/7)

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