Let x2+y2−4x−2y−11=0 be a circle. A pair of tangents from the point (4, 5) with a pair of radii form a quadrilateral of area ___.
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Solution
The equation of the circle is x2+y2−4x−2y−11=0.
Its center is (2, 1) and radius is √4+1+11=4=BC. AC=2√5...(FromDistanceformula)∴AB=2...(FromrightΔABC)∴AreaofquadrilateralABCD=2×(AreaofΔABC)=2×12×AB×BC=2×12×2×4=8sq.units