CLASS-6
CIRCLE - INTERIOR & EXTERIOR
CIRCLE - INTERIOR & EXTERIOR -
In geometry, when referring to the interior and exterior of a circle, we typically mean the regions inside and outside the circle's circumference, respectively.
Interior Of A Circle:-
The interior of a circle refers to the space enclosed by the circle's circumference. This area includes all points that lie within the circle. When discussing the interior of a circle, we consider points that are inside the boundary defined by the circle.
In above picture, a point P lies outside a circle if and only if its distance from the centre of the circle is less than the radius of the circle. In the adjoining figure, CP < r, so P lies inside a circle with centre C, and radius r.
Exterior Of A Circle:-
The exterior of a circle refers to the space outside the circle's circumference. This area includes all points that lie outside the circle. When discussing the exterior of a circle, we consider points that are beyond the boundary of the circle.
In above picture we can observe that, a point P lies outside a circle if and only if its distance from the centre of the circle is greater than the radius of the circle. In the above picture, CP > r, so P lies outside a circle with centre C and radius r. The collection of all points P of the plane such that CP > r form the exterior of the circle.
Understanding the interior and exterior of a circle is fundamental in various geometric and mathematical contexts. For example, when considering regions for shading or locating points relative to a circle, distinguishing between the interior and exterior helps define relationships and solve problems effectively.