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.

Consider the traingle having vertices O(0,0),A(2,0) , and B(1,sqrt3) . Also b le"min" {a_1,a_2,a_3....a_n} means b le a_1 when a_1 is least, b le a_2 when a_2 is least, and so on. Form this, we can say b le a_1,b le a_2,.....b le a_n . Let R be the region consisting of all those points P inside DeltaOAB which satisfy d(P,OA)le "min"[d(P,OB),d(P,AB)] , where d denotes the distance from the point to the corresponding line. then the area of the region R is

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 Area of region reperesenting all possible position of point P is equal to

A(3, 4),B(0,0) and c(3,0) are vertices of DeltaABC. If 'P' is the point inside the DeltaABC , such that d(P, BC)le min. {d(P, AB), d (P, AC)} . Then the maximum of d (P, BC) is.(where d(P, BC) represent distance between P and BC) .

The vertices of a triangle are O(0,0),\ A(a ,0)a n d\ B(0, b) . Write the coordinates of its circumcentre.

Let O(0,0),P(3,4), and Q(6,0) be the vertices of triangle O P Q . The point R inside the triangle O P Q is such that the triangles O P R ,P Q R ,O Q R are of equal area. The coordinates of R are a. (4/3,3) b. (3,2/3) c. (3,4/3) d. (4/3,2/3)

Let O(0,0),P(3,4), and Q(6,0) be the vertices of triangle O P Q . The point R inside the triangle O P Q is such that the triangles O P R ,P Q R ,O Q R are of equal area. The coordinates of R are (4/3,3) (b) (3,2/3) (3,4/3) (d) (4/3,2/3)

Let AP and BQ be two vertical poles at points A and B, respectively. If A P = 16 m , B Q = 22 m a n d A B = 20 m , then find the distance of a point R on AB from the point A such that R P^2+R Q^2 is minimum.

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

Let P(x) denote the probability of the occurrence of event xdot Plot all those point (x , y)=(P(A),P(B)) in a plane which satisfies the conditions, P(AuuB)geq3//4a n d1//8lt=P(AnnB)lt=3//8

Let O-=(0,0),A-=(0,4),B-=(6,0)dot Let P be a moving point such that the area of triangle P O A is two times the area of triangle P O B . The locus of P will be a straight line whose equation can be