Question

In problem no. 7, if the point 'P' moves in such a way that d(P, OA) < min {d (P, OB}, d(P, AB)}, then area of the region representing all possible positions of the point 'P' is equal to

• A. $\sqrt { 3 }$sq. units
• B. $\sqrt { 6 }$sq. units
• C. $\frac { 1 } { \sqrt { 3 } }$sq. units
• D. $\frac { 1 } { \sqrt { 6 } }$ sq. union

Answer 1

Answer: (C)

$\frac { 1 } { \sqrt { 3 } }$sq. units

Answer 2

We must have d(P, OA) ≤ d(P, OB) as well as d(P, OA) ≤ d(P, AB).

Thus, 'P' lies either on or below the angle bisectors of ∠BOA and ∠BAO. Required area = $\frac { 1 } { 3 } \cdot \Delta _ { \mathrm { OAB } } = \frac { 1 } { \sqrt { 3 } }$ sq. units.