Circles
Locus of Circumcentre
Grade 11
Question:
<p>If from a moving point P on \(x^2 + y^2 = 4\) tangents PA and PB are drawn to \(x^2 + y^2 = a^2\), then the locus of the circumcentre of triangle PAB, is \((0 < |a| < 2)\):</p>
<p>(a) \(x^2 + y^2 = a^2 + 4\)</p>
<p>(b) \(x^2 + y^2 = 4 - a^2\)</p>
<p>(c) \(x^2 + y^2 = 1\)</p>
<p>(d) \(x^2 + y^2 = 2\)</p>
Step-by-Step Solution
Key Concept: The circumcentre of the triangle formed by tangent points lies on a fixed circle determined by the radical axis of the two given circles.
<p>The circumcentre of triangle PAB lies on the radical axis of the two circles. Using properties of tangents and circles, the locus is \(x^2 + y^2 = 1\).</p>
Correct Answer: C