Two circles are concentric A chord of the larger circle is tangent to the smaller If the area - Maths - Areas Related to Circles

Question

Two circles are concentric A chord of the larger circle is tangent
to the smaller If the area of the annulus is
A, express the length of the chord in terms of A

Lovina Kansal · Accepted Answer

Dear student
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_5827082a3a0b1%20png"
style="width: 235px; height: 219px;">
Let the radius of the smaller circle be rand radius of the larger circle be RGiven,  area of annulus =Aand also we know that, A=πR2-πr2⇒A=πR2-r2⇒R2-r2=Aπ⇒R2-r2=Aπ  
(1)Now consider △OO'BBy pythagoras theoremOB2=OO'2+O'B2⇒R2=r2+O'B2⇒R2-r2=O'B2⇒R2-r2=O'BSo, AB=2O'B⇒AB=2×Aπ   from (1)
Regards

Two circles are concentric. A chord of the larger circle is tangent to the smaller. If the area of the annulus is A, express the length of the chord in terms of A.

Two circles are concentric. A chord of the larger circle is tangent to the smaller. If the area of the annulus is
A, express the length of the chord in terms of A.