If P is a point which moves inside an equilateral triangle of side length ' a ' such that it is nearer to any angular bisector of the triangle than to any of its sides, then the area of the

Question

If P is a point which moves inside an equilateral triangle of side length ' a ' such that it is nearer to any angular bisector of the triangle than to any of its sides, then the area of the region in which P lies is ____ sq units

TestHub · Accepted Answer

Shaded area is the region traced by P , its area $= △ A BC - 3△ A B D$

$= \frac{3}{4} a^{2} - \frac{3}{2} a \times \frac{a}{2} tan 1 5^{0} == \frac{3}{2} a^{2} (\frac{3 - 1}{3 + 1})$

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