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Find the area of the triangle formed by joining the origin to the point(s) where the line x*sqrt(5) + 2y = 3*sqrt(5) meets the circle x² + y² = 10.

1. 3
2. 4
3. 5
4. 6

Correct answer: 5

Solution

Distance from origin to the line is p = 3*sqrt(5)/sqrt(5+4) = 3*sqrt(5)/3 = sqrt(5). Half-chord = sqrt(r² - p²) = sqrt(10-5) = sqrt(5), so chord = 2*sqrt(5). Area = (1/2)*chord*p = (1/2)*2*sqrt(5)*sqrt(5) = 5.

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