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CGP EDU Academic Team
Published on: August 13, 2026
Let A be the centre of the circle x² + y² − 2x − 4y − 20 = 0. Suppose that the tangents at the points B (1, 7) & D (4, − 2) on the circle meet at the point C. Find the area of the quadrilateral ABCD.
Text Solution
Verified by ExpertsThe correct answer is:
75
(75)Given circle x 2 + y 2 – 2x – 4y – 20 = 0
Tangents at B(1, 7) is
x + 7y – (x + 1) – 2(y + 7) – 20 = 0
5y – 35 = 0 ⇒ y = 7
at D (4, –2)
4x – 2y – (x + 4) – 2(y – 2) – 20 = 0
3x – 4y = 20
Hence c(16, 7)
Area of quadrilateral ABCD = AB × BC = 5 × 15 = 75 square units.
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