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Chords are drawn from the origin to the circle (x - 1)² + y² = 1. The locus of the midpoints of these chords has the equation x² + y² - lambda*x = 0. What is the value of lambda?

1. 1
2. 2
3. 3
4. 4

Correct answer: 1

Solution

The perpendicularity condition gives k² + h(h-1) = 0, i.e. x² + y² - x = 0, so lambda = 1.

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