A computer graphics program displays images on a rectangular screen whose coordinate system has the origin at the bottom-left corner. The screen is 800 pixels wide and 600 pixels high. A circular icon of radius 80 pixels is drawn with its centre at the point A (100, 150). Another circular icon of radius 100 pixels is drawn with its centre at the point B (250, 230). Determine:
whether any part of either circle lies outside the screen.
No, neither circle lies outside the screen.
whether the two circles intersect each other.
Yes, the two circles intersect each other.
Explanation
To determine if any part of a circle lies outside the rectangular screen, we compare the extreme coordinates of the circle (centre ± radius) with the screen boundaries (0 to 800 for x, 0 to 600 for y). For both circles, all extreme points fall within these boundaries. To check for intersection, we calculate the distance between the centres using the distance formula and compare it with the sum and difference of their radii. If the distance is strictly between the difference and sum of the radii, the circles intersect at two points.