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A circle passes through the points (-1, 1), (0, 6) and (5, 5). Find the point(s) on this circle at which the tangent is parallel to the line joining the origin to the centre of the circle.
- (6, 4) and (-2, 2)
- (4, 6) and (-2, 2)
- (6, 4) and (2, -2)
- (5, 5) and (-1, 1)
Correct answer: (6, 4) and (-2, 2)
Solution
The circle is x² + y² - 4x - 6y + 5 = 0 with centre (2, 3). The diameter through the centre perpendicular to OC meets the circle at (6, 4) and (-2, 2), where the tangents are parallel to OC.
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