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Tangents are drawn to the two concentric circles x² + y² = a² and x² + y² = b² such that the two tangents are perpendicular to each other. The locus of their point of intersection is a third concentric circle. Find its radius.
- sqrt(a² + b²)
- sqrt(a² - b²)
- a + b
- (a + b)/2
Correct answer: sqrt(a² + b²)
Solution
The perpendicular distances from the common centre to the two tangents equal the respective radii a and b, and because the tangents meet at right angles these two distances together with OP form a rectangle, giving OP² = a² + b², so the locus is a circle of radius sqrt(a² + b²).
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