<p>Let P be situated at a distance 'd' from centre O. Which of the following does not equal the product (PQ)(PR), where T is a point on C and PT is tangent to C:</p>
Step-by-Step Solution
Key Concept: The power of a point P with respect to circle C is constant: (PQ)(PR) = d² - r² for any secant, and equals (PT)² for any tangent.
<p><strong>Analysis:</strong> By power of a point theorem, \((PQ)(PR) = d^2 - r^2\). Also, \((PT)^2 = d^2 - r^2\) since PT is a tangent. For option (c), using \((PS)^2 - (QS)(RS)\): since S is the midpoint of QR, we have \((QS)(RS) = (PS)^2 - r^2\) (from the perpendicularity property), so this also equals \(d^2 - r^2\). However, \((PS)^2\) itself does not equal \(d^2 - r^2\) unless specific conditions are met.</p>
Correct Answer: D