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.

Let O(0, 0), A(2,0) and B(1,(1)/(sqrt(3))) be the vertices of a triangle. Let R be the region consisting of all those points P inside Delta OAB satisfying. d(P,OA) lr min {d(P,OB), d(P,AB)} , where d denotes the distance from the point P to the corresponding line. Let M be peak of region R. The perimeter of region R is equal to

Let ABC be a triangle with vertices A-=(6,2sqrt(3)+1)) ) B-=(4,2) and C-=(8,2). Let R be the region consisting of all those points P inside Delta ABC which satisfyd (P,BC)>=max{d(P,AB);d(P,AC)}, where d(P,L) denotes the distance of the point from the line L,then

Let O(0.0),A(6,0) and B(3,sqrt3) be the vertices of triangle OAB. Let R those points P inside triangle OAB which satisfy d(P, OA) minimum (d(P,OB),d(P,AB) where d(P, OA), d(P, OB) and d(P, AB) represent the distance of P from the sides OA, OB and AFB respectively. If the area of region R is 9 (a -sqrtb) where a and b are coprime, then find the value of (a+ b)

Let O(0,0),A(2,0) be the vertices of an isosceles triangle inscribed in an ellipse (x-1)^(2)+3y^(2)=1. Let s represents the region consisting all those points P inside the given triangle which stales that,Distance of pistance of point p from the other two mides of the triangle

Let d(P, OA) le min {d (P, AB), d(P, BC), d (P, OC)} where d denotes the distance from the point to the corresponding line and S be the region consisting of all those points P inside the rectangle OABC such that O = (0, 0), A = (3, 0), B = (3, 2) and C = (0, 2), which satisfy the above relation, then area of the region S is

Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR are of equal area. The coordinates of R are

Let O(0,0),A(2,0),B(1,(1)/(sqrt(3))) distance of P from the side OA is less than its distance from the syme vertices of a triangle.A point P moves inside the triangle.A point P distance of P from the side OA is less than its distance from the sides OB and AB.The area traced by Pis

Two points O(0,0) and A(3,sqrt(3)) with another point P form an equilateral triangle. Find the coordinates of P.