Let be a triangle with vertices

MATHEMATICS · Subjective · ISC · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

Let

ABC

be a triangle with vertices

A \equiv (6, 2(\sqrt{3} + 1))

B \equiv (4, 2)

and

C \equiv (8, 2)

. Let

R

be the region consisting of all those points

P

inside

\triangle ABC

which satisfy

d(P, BC) \ge \text{max} \{d(P, AB), d(P, AC)\}

, where

d(P, L)

denotes the distance of the point

P

from the line

L

. Sketch the region

R

and find its area.