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Let A be the centre of the circle x² + y² - 2x - 4y - 20 = 0. The tangents to the circle at the points B(1, 7) and D(4, -2) on the circle meet at point C. Find the area of the quadrilateral ABCD.

1. 50
2. 75
3. 100
4. 150

Correct answer: 75

Solution

The centre is A(1,2) with radius 5. Tangents at B and D meet at C(16,7). Each right-triangle ABС and ADC has legs 5 and 15, giving area 75/2 each; total area = 75.

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