Multiple choice

Given two concentric circles with centre P, AC is a chord of the larger circle tangent to the smaller at B. If |BC| = 2 units, find the area of the annulus between the circles in square units.

  1. 4π

  2. 6π

  3. 8π

  4. 16π
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A Correct answer
Explanation

Let R, r be the radii of bigger & smaller circles respectively. In ΔABP R2 = r2 + (AB)2 ………… (1) As BC = 2 Ac is a chord PB is perpendicular to it & must bisect the chord. AB = BC = 2 From (1) R2 - r2 = 4 Area of the annulus = πR2 - πr2 = π(R2 - r2) = 4π

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