Circles
Geometric Properties of Circles
Grade 11
Question:
<p>Let <span style="display: block;"><strong>S</strong> = {(x, y) : (√5 - 1)x - √(10 + 2√5) y ≥ 0, (√5 - 1)x + √(10 + 12√5) y ≥ 0, x² + y² ≤ 9}</span>then the diameter of S is:</p>
<p>(a) <span>3(√5 - 1)/2</span></p>
<p>(b) 3(√5 - 1)</p>
<p>(c) 3√2</p>
<p>(d) 3</p>
Step-by-Step Solution
Key Concept: Find the intersection of linear inequalities with a circular region and determine the maximum distance across the feasible region.
<p>The set S represents the intersection of a circular disk of radius 3 centered at the origin with a region bounded by two lines. The diameter of S is determined by the constraint with the smallest diameter.</p>
Correct Answer: D