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Let A be the centre of the circle x² + y² - 2x - 4y - 20 = 0, and let B(1, 7) and D(4, -2) be points on this circle. Tangents drawn at B and D meet at point C. Find the area of quadrilateral ABCD.
- 150
- 75
- 75/2
- none of these
Correct answer: 75
Solution
The circle has centre (1,2) and radius 5. Tangents from C touch at B and D, so AB and AD (radii) are perpendicular to the tangents, making ABCD a kite of two right triangles. Computing gives area 75.
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