A square A BC D is inscribed in a circle of radius 4 . A point P moves inside the circle such that d ( P , A B ) ≤ min ( d ( P , BC ) , d ( P , C D ) , d ( P , D A )) , where d ( P , A B ) is the distance of a point P from line A B . The area of region covered by moving point P is (in sq. units)

Put the square's sides on x = ± a , y = ± a , where a = 2 2 . The inequalities reduce to y ≥ ∣ x ∣ . Inside the circle this is the sector between the two radii to A and B , whose central angle is π /2 . Its area is 4 1 π ( 4 ) 2 = 4 π .

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MathematicsCircleGeneral, Basic geometries, Definition Diametrical form of circleMedium2 minQB

MathematicsMediumsingle choice

A square $A BC D$ is inscribed in a circle of radius 4 . A point $P$ moves inside the circle such that $d (P, A B) \leq$ $min (d (P, BC), d (P, C D), d (P, D A))$ , where $d (P, A B)$ is the distance of a point $P$ from line $A B$ . The area of region covered by moving point $P$ is (in sq. units)

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Solution:

Put the square's sides on $x = \pm a, y = \pm a$ , where $a = 22$ . The inequalities reduce to $y \geq ∣ x ∣$ . Inside the circle this is the sector between the two radii to $A$ and $B$ , whose central angle is $π /2$ . Its area is $\frac{1}{4} π (4)^{2} = 4 π$ .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:General, Basic geometries, Definition Diametrical form of circle

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