Home
Class 12
MATHS
Let O(0,0),A(2,0),a n dB(1 1/(sqrt(3))) ...

Let `O(0,0),A(2,0),a n dB(1 1/(sqrt(3)))` be the vertices of a triangle. Let `R` be the region consisting of all those points `P` inside ` O A B` which satisfy `d(P , O A)lt=min[d(p ,O B),d(P ,A B)]` , where `d` denotes the distance from the point to the corresponding line. Sketch the region `R` and find its area.

A

`2-sqrt(3)`

B

`2+sqrt(3)`

C

`4+3sqrt(3)`

D

`2+4sqrt((2-sqrt(3)))`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|5 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise EXERCISE : 5|2 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|7 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|20 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|37 Videos

Similar Questions

Explore conceptually related problems

Let (4, 2), B (6, 5) and C (1, 4) be the vertices of triangleABC . :- The median from A meets BC at D. Find the coordinates of the point D.

Let P-=(-1,0),Q-=(0,0), "and " R-=(3,3sqrt(3)) " be three points". Then the equation of the bisector of angle PQR is

The vertices of a triangleOBC are O(0,0) , B(-3,-1), C(-1,-3) . Find the equation of the line parallel to BC and intersecting the sides OB and OC and whose perpendicular distance from the origin is 1/2 .

Consider a DeltaOAB formed by the point O(0,0),A(2,0),B(1,sqrt(3)).P(x,y) is an arbitrary interior point of triangle moving in such a way that d(P,OA)+d(P,AB)+d(P,OB)=sqrt(3), where d(P,OA),d(P,AB),d(P,OB) represent the distance of P from the sides OA,AB and OB respectively If the point P moves in such a way that d(P,OA)lemin(d(P,OB),d(P,AB)), then the area of region representing all possible position of point P is equal to

The area of the triangle formed by the points P(0,1),Q(0,5) and R(3,4) is

Let L_1=0a n dL_2=0 be two fixed lines. A variable line is drawn through the origin to cut the two lines at R and SdotPdot is a point on the line A B such that ((m+n))/(O P)=m/(O R)+n/(O S)dot Show that the locus of P is a straight line passing through the point of intersection of the given lines R , S , R are on the same side of O)dot

If the coordinates of the mid-points of the sides of a triangle are (1,2)(0,-1)a n d(2,-1)dot Find the coordinate of its vertices.

If a circle passes through the point (0,0),(a ,0)a n d(0, b) , then find its center.

For points P-=(x_1, y_1) and Q-=(x_2, y_2) of the coordinate plane, a new distance d(P ,Q)=|x_1-x_1|+|y_1-y_2| . Let O=(0,0) and A=(3,2) . Prove that the set of points in the first quadrant which are equidistant (with respect to the new distance) from O and A consists of the union of a line segment of finite length and an infinite ray. Sketch this set in a labelled diagram.