Tangents are drawn from point (4, 5) to circle {x^2} + {y^2} - 4x - 2y - 11 = 0 . area of quadrilate

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10-1.Circle and System of Circles

hard

The tangents are drawn from the point $(4, 5)$ to the circle ${x^2} + {y^2} - 4x - 2y - 11 = 0$. The area of quadrilateral formed by these tangents and radii, is .............. $\mathrm{sq.\, units}$

A

$15$

B

$75$

C

$8$

D

$4$

(IIT-1985)

Solution

(c) Length of each tangent

${L^2} = {(4)^2} + {(5)^2} – (4 \times 4) – (2 \times 5) – 11$

$L = 2$

$r = \sqrt {{2^2} + {1^2} – ( – 11)} $

$r = 4$

Area $ = L \times r = 8\ sq.\ units.$

Standard 11

Mathematics

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