Let $A$ be the centre of the circle ${ x }^{ 2 }+{ y }^{ 2 }-2x-4y-20=0$. Let $B(1,7)$ and $D(4,-2)$ be two points on the circle such that tangents at $B$ and $D$ meet at $C$. The area of the quadrilateral $ABCD$ is
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$150$ sq. units
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$50$ sq. units
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$75$ sq. units
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$70$ sq. units
C
Correct answer
Explanation
The circle equation x^2 + y^2 - 2x - 4y - 20 = 0 has center A(1, 2) and radius r = 5. Points B and D lie on the circle, and the tangents at these points meet at C. The area of the kite ABCD is twice the area of triangle ABD or can be calculated using the properties of tangents.