(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 →

If the equation of the incircle of an equilateral triangle is $x^2 + y^2 + 4x - 6y + 4 = 0$,then the equation of its circumcircle is:

Difficult

View Solution

The angle of intersection of the circles $x^2 + y^2 + 8x - 2y - 9 = 0$ and $x^2 + y^2 - 2x + 8y - 7 = 0$ is ............ $^o$.

Medium

View Solution

If a straight line through $C(-\sqrt{8}, \sqrt{8})$ making an angle of $135^\circ$ with the $x$-axis cuts the circle $x = 5\cos\theta, y = 5\sin\theta$ at points $A$ and $B$,then the length of $AB$ is

Medium

View Solution

For the circle $x^2+y^2-9=0$,find the equation of the chord having $(1,2)$ as its mid-point.

EasyAP EAMCET 2020

View Solution

The image of the point $(3, 4)$ with respect to the radical axis of the circles $x^2 + y^2 + 8x + 2y + 10 = 0$ and $x^2 + y^2 + 7x + 3y + 10 = 0$ is

MediumAP EAMCET 2022

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

If the equation of the incircle of an equilateral triangle is $x^2 + y^2 + 4x - 6y + 4 = 0$,then the equation of its circumcircle is:

The angle of intersection of the circles $x^2 + y^2 + 8x - 2y - 9 = 0$ and $x^2 + y^2 - 2x + 8y - 7 = 0$ is ............ $^o$.

If a straight line through $C(-\sqrt{8}, \sqrt{8})$ making an angle of $135^\circ$ with the $x$-axis cuts the circle $x = 5\cos\theta, y = 5\sin\theta$ at points $A$ and $B$,then the length of $AB$ is

For the circle $x^2+y^2-9=0$,find the equation of the chord having $(1,2)$ as its mid-point.

The image of the point $(3, 4)$ with respect to the radical axis of the circles $x^2 + y^2 + 8x + 2y + 10 = 0$ and $x^2 + y^2 + 7x + 3y + 10 = 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module