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:

(A) whether any part of either circle lies outside the screen.

(B) whether the two circles intersect each other.

The visible screen is the rectangle $0 \leq x \leq 800$ , $0 \leq y \leq 600$.

(A) A circle lies entirely on the screen if its centre is at least $r$ pixels from every edge.

Circle 1: centre A(100, 150), $r = 80$ .

Distance from left edge ( $x = 0$ ): $100 \geq 80$

Distance from right edge ( $x = 800$ ): $700 \geq 80$

Distance from bottom edge ( $y = 0$ ): $150 \geq 80$

Distance from top edge ( $y = 600$ ): $450 \geq 80$

So, circle 1 is fully inside the screen.

Circle 2: centre B(250, 230), $r = 100$ .

From left: $250 \geq 100$

From right: $550 \geq 100$

From bottom: $230 \geq 100$

From top: $370 \geq 100$

So, circle 2 is also fully inside the screen.
Hence, neither circle has any part outside the screen.

(B) Two circles intersect if the distance between their centres satisfies $|r_1 - r_2| \leq d \leq r_1 + r_2$ .

$$\begin{aligned} AB &= \sqrt{(250 - 100)^2 + (230 - 150)^2} \\ &= \sqrt{150^2 + 80^2} = \sqrt{22500 + 6400} \\ &= \sqrt{28900} = 170 \text{ pixels}. \end{aligned}$$

$$r_1 + r_2 = 80 + 100 = 180.$$

$$|r_1 - r_2| = |80 - 100| = 20.$$

Since $20 < 170 < 180$ , the distance between centres lies between the difference and sum of radii, so the circles intersect at two points.