To find:The area of region common to both circles.

Brennan Flores

Brennan Flores

Answered question

2021-08-13

To find:The area of region common to both circles.

Answer & Explanation

Clara Reese

Clara Reese

Skilled2021-08-14Added 120 answers

Explanation of solution
image

image

2021-12-24

Now taking sector OAPB

sinOBX=36

sinOBX=0.5

mOBX=30 and

cos30=XB6

XB=33

AX=XB=33 and

AX=XB=12AB

AB=2 AX

AB=(2)33

AB=63

Now in triangle AOB

AOB+OBX+OAX=180

AOB+60=180

AOB=120

so mAB=120

let AB=x

Now area of sector

AAOB=x360πr2

AAOB=120360π(6)2

AAOB=12π

Now area of shaded region in OAPB is 

A=12π93cm3

Similarly in the right circle

Shaded region is also A=12π93cm2

Thus, common shaded area

A=(12π93)+(12π93)cm2

A=24π183  cm2

Hence, A=24π183  cm2

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