(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_

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(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

Difficult

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

KVPY 2009 All KVPY

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

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

10-1.Circle and System of Circles

Subtopic

Geometrical problems regarding circle and its properties

Previous Year

KVPY 2009 Paper All KVPY years →

The maximum area of a rectangle inscribed in the circle $(x+1)^{2}+(y-3)^{2}=64$ is

DifficultKCET 2018

View Solution

If the lengths of the chords intercepted by the circle $x^2 + y^2 + 2gx + 2fy = 0$ from the coordinate axes are $10$ and $24$ respectively,then the radius of the circle is:

Easy

View Solution

The length of the intercept that the circle $x^2 + y^2 + 10x - 6y + 9 = 0$ makes on the $x$-axis is:

Easy

View Solution

If the two circles $(x - 1)^2 + (y - 3)^2 = r^2$ and $x^2 + y^2 - 8x + 2y + 8 = 0$ intersect at two distinct points,then:

Difficult

View Solution

If the circles $S \equiv x^2+y^2-14x+6y+33=0$ and $S' \equiv x^2+y^2-a^2=0$ where $a \in \mathbb{N}$ have $4$ common tangents,then the possible number of values of $a$ is:

EasyAP EAMCET 2024

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

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

Similar Questions

The maximum area of a rectangle inscribed in the circle $(x+1)^{2}+(y-3)^{2}=64$ is

If the lengths of the chords intercepted by the circle $x^2 + y^2 + 2gx + 2fy = 0$ from the coordinate axes are $10$ and $24$ respectively,then the radius of the circle is:

The length of the intercept that the circle $x^2 + y^2 + 10x - 6y + 9 = 0$ makes on the $x$-axis is:

If the two circles $(x - 1)^2 + (y - 3)^2 = r^2$ and $x^2 + y^2 - 8x + 2y + 8 = 0$ intersect at two distinct points,then:

If the circles $S \equiv x^2+y^2-14x+6y+33=0$ and $S' \equiv x^2+y^2-a^2=0$ where $a \in \mathbb{N}$ have $4$ common tangents,then the possible number of values of $a$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module