Circle And System Of Circles Question 7
Question: . If OA and OB are the tangents from the origin to the circle $ x^{2}+y^{2}+2gx+2fy+c=0 $ and C is the centre of the circle, the area of the quadrilateral $ OACB $ is
Options:
A) $ \frac{1}{2}\sqrt{c(g^{2}+f^{2}-c)} $
B) $ \sqrt{c(g^{2}+f^{2}-c)} $
C) $ c\sqrt{g^{2}+f^{2}-c} $
D) $ \frac{\sqrt{g^{2}+f^{2}-c}}{c} $
Show Answer
Answer:
Correct Answer: B
Solution:
Area of quadrilateral $ =2 $ [area of $ \Delta OAC $ ] $ =2.\frac{1}{2}OA\ .\ AC=\sqrt{S_1}.,\sqrt{g^{2}+f^{2}-c} $ Point is (0, 0)
$ \Rightarrow S_1=c $ .
$ \therefore $ Area $ =\sqrt{c}.\sqrt{g^{2}+f^{2}-c} $ .
BETA
