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an equilateral triangle is inscribed in a circle of radius 2 cm if P lies inside the triangle then the minimum sum of distances of P from the sides of the triangle is _______

an equilateral triangle is inscribed in a circle of radius 2 cm if P lies inside the triangle then the minimum sum of distances of P from the sides of the triangle is _______

Grade:12

1 Answers

Roshan Mohanty
64 Points
8 years ago

see for the sum of distances to be minimum i think the distance to each side should be minimum...
Which means the point p should be the intersection point of the three altitudes..
as it is given an equilateral triangle so the point p will be the centre. . .
If you take a small triangle with two sides as the radius and the distance from the side..then u get a relation
2 * sin 30 = Distance req
so d=1
so now the minimum sum = 1+1+1 =3
i hope its  correct 

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