The circle x2 + y2 = 1 cuts the x-axis at P and Q. another circle with centre at Q and variable radius intersects the first circle at R above the x-axis and the line segment PQ at S. Find the maximum area of the triangleQSR.
The given circle is x2 + y2 = 1
With centre at O (0, 0) and radius 1. It cuts x-axis at the points when y = 0 then x = ± 1 i.e., at P(–1, 0) and Q(1, 0).
Equation of circle with centre at Q(1, 0) and radius r is
(x – 1)2 + (y – 0)2 = r2 …(2) (0 < r < 2)
Solving (1) and (2), we get
But R above the x-axis.
For maximum and minimum area,
∴ A is maximum. Hence âˆ† is also maximum.
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