Circle 5 Question 14
14. Let $x^{2}+y^{2}-4 x-2 y-11=0$ be a circle. A pair of tangents from the point $(4,5)$ with a pair of radii form a quadrilateral of area… .
$(1985,2 M)$
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Answer:
Correct Answer: 14. 8 sq units
Solution:
- Here, length of tangent $A B$
$$ =\sqrt{4^{2}+5^{2}-4(4)-2(5)-11}=2 $$
$\therefore$ Area of quadrilateral $A B O C=2$ area of $\triangle A B O$
$$ \begin{aligned} & =2 \cdot \frac{1}{2}(A B)(O B) \\ & =2 \cdot 4=8 sq units \end{aligned} $$
