Question

Let O (0,0), A (2,0) and B(1, 1/√3) be the vertices of a triangle. Let R be the region consisting of all those points P inside ΔOAB which satisfy d (P, OA) ≥ min {d (P,OB), d(P,AB)}, where d denotes the distance from the point to the corresponding line. Sketch the region R and find its area.

Answer 1

Let the coordinate of P be (x, y).

From above discussion P moves inside the Δ as shown,