(B) The set of points $R$ closer to $O$ than to any point $P_i$ is defined by the intersection of the half-planes $H_i = \{X : dist(X, O) < dist(X, P_

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(B) The set of points $R$ closer to $O$ than to any point $P_i$ is defined by the intersection of the half-planes $H_i = \{X : dist(X, O) Each boundary line $dist(X, O) = dist(X, P_i)$ is the perpendicular bisector of the segment $OP_i$.Since there are $5$ such points $P_i$ arranged symmetrically around $O$,the intersection of these $5$ half-planes forms a regular pentagon centered at $O$.Thus,$R$ is a pentagonal region.

Class 11 Mathematics 10-1.Circle and System of Circles Geometrical problems regarding circle and its properties

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Let $P_1, P_2, P_3, P_4, P_5$ be five equally spaced points on the circumference of a circle of radius $1$,centred at $O$. Let $R$ be the set of points in the plane of the circle that are closer to $O$ than any of $P_1, P_2, P_3, P_4, P_5$. Then,$R$ is a

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A
circular region
B
pentagonal region
C
rectangular region
D
oval region that is not circular

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10-1.Circle and System of Circles

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Geometrical problems regarding circle and its properties

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Let $P_1, P_2, P_3, P_4, P_5$ be five equally spaced points on the circumference of a circle of radius $1$,centred at $O$. Let $R$ be the set of points in the plane of the circle that are closer to $O$ than any of $P_1, P_2, P_3, P_4, P_5$. Then,$R$ is a

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