Problem 1

Geometry Level 5

Let $P_1, P_2, P_3, P_4, P_5$ be 5 equally spaced points on the circumference of a unit circle with origin $O$ . Let $R$ be the set of points in the plane of the circle that are closer to $O$ than any of these 5 points.

$R$ must be a $\text{\_\_\_\_\_\_\_\_\_\_\_} .$ .

Pentagonal region Circular region Rectangular region Oval shaped but not a circle

1 solution

Niranjan Khanderia
Jan 6, 2017

Pi...i=1, 2, 3, 4, 5, are vertices of a pentagon. Any point nearer to the center will be with in the pentagon. Except the points between pentagon and the circumcircle. However, out of the given answers this answer that is meaningful.

why not the circular region. as the equation of that circle would be x^2+y^2<1

Deepansh Jindal - 4 years, 5 months ago

Another way would be to take the points pair by pair P1O, P2O, . . . for each pair, the perpendicular bisector divides the plane into two halves - one closer to O and the other closer to Pi. There will be five such half planes (bound by the perpendicular bisectors) common area (intersection) of which will be a pentagon.

Ujjwal Rane - 4 years, 5 months ago

Problem 1

1 solution

0 pending reports