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The angle between the tangents drawn from the origin (0, 0) to the circle x² + y² + 4x + 8y + c = 0 is pi/2. Find the value of c.

1. 10
2. 20
3. -10
4. 0

Correct answer: 10

Solution

For a 90 deg angle between tangents, d = r*sqrt(2), giving 20 = 2(20 - c), so c = 10.

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