<p>The value of |a| for which the common chord of the circles \(x^2 + y^2 = 8\) and \((x - a)^2 + y^2 = 8\) subtends a right angle at the origin are ............</p>
Step-by-Step Solution
Key Concept: The common chord subtends a right angle at the origin means if P is on the chord, angle OPA = 90°. Use the chord equation and perpendicularity condition.
<p><strong>Solution approach:</strong> For two circles to have a common chord that subtends a right angle at the origin, if P is a point on the common chord, then OP must satisfy the condition that the angle subtended is 90°. Using the property that the common chord equation is found by subtracting the circle equations, and applying the right angle condition at origin, we get |a| = 4.</p>
Correct Answer: 4