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CGP EDU Academic Team
Published on: August 13, 2026
P is a variable point on the circle with centre C and radius 9 units. CA and CB are perpendiculars from C on x-axis and y-axis respectively, then centroid of the triangle PAB always lies on a circle of radius.........
Text Solution
Verified by ExpertsThe correct answer is:
3
Ans. 3
Sol.
The given circle is (x – a) 2 + (y – b) 2 = 81
Let point P(a + 9cos θ , b + 9sin θ ) be lie on it. Let G(h, k) be the centroid of Δ APB, then
3h = 2a + 9cos θ and 3k = 2b + 9sin θ
eliminate θ :
(3h – 2a) 2 + (3k – 2b) 2 = 81
Locus of G is : 
= 9
required radius = 3
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