TEXTBOOK REFERENCE · GANITA MANJARI
End-of-Chapter Q15 · Open official source ↗
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 . Another circular icon of radius 100 pixels is drawn with its centre at the point B . Determine:
(i) whether any part of either circle lies outside the screen.
(ii) whether the two circles intersect each other.
AIMS worked solution
AIMS SOLUTION / EXPLANATION
A · B
Given:
Origin at the screen’s bottom-left corner.
To Find:
Containment and intersection.
Property:
A circle’s bounds are centre ± radius. Two circles cross twice if | − | < AB < + .
Solution:
Circle A: x from 20 to 180; y from 70 to 230. Circle B: x from 150 to 350; y from 130 to 330. All bounds fit the screen.
AB = = = 170 pixels.
The radius difference is 20 and the sum is 180. Since 20 < 170 < 180, the circles intersect twice.
Results:
Both circles lie inside the screen and intersect in two points.
Compare your reasoning, not only the answer. Viewing this solution does not record completion or mastery.
Compare the reasoning with your own work. Reading a solution does not record mastery.
Textbook completion: not tracked yet. Your written response stays in this page’s current session.