Trigonometric Equations Question 181
Question: If R is the radius of the circumcircle of the $ \Delta ABC $ and $ \Delta $ is its area, then
[Karnataka CET 2000]
Options:
A) $ R=\frac{a+b+c}{\Delta } $
B) $ R=\frac{a+b+c}{4\Delta } $
C) $ R=\frac{abc}{4\Delta } $
D) $ R=\frac{abc}{\Delta } $
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Answer:
Correct Answer: C
Solution:
- Area of the triangle ABC $ (\Delta )=\frac{bc}{2}\sin A. $ From the sine formula, a = 2R sin A or $ \sin A=\frac{a}{2R}. $
$ \Rightarrow \Delta =\frac{1}{2}bc,.,\frac{a}{2R}=\frac{abc}{4R},\text{or }R=\frac{abc}{4\Delta }. $
BETA
