JEE PYQ: Properties Of Triangle Question 7
Question 7 - 2019 (11 Jan Shift 1)
In a triangle, the sum of lengths of two sides is $x$ and the product of the lengths of the same two sides is $y$. If $x^2 - c^2 = y$, where $c$ is the length of the third side of the triangle, then the circumradius of the triangle is:
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(1) $\frac{3}{2}y$
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(2) $\frac{c}{\sqrt{3}}$
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(3) $\frac{c}{3}$
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(4) $\frac{y}{\sqrt{3}}$
Show Answer
Answer: (2) $\frac{c}{\sqrt{3}}$
Solution
$(a+b)^2 - c^2 = ab \Rightarrow 4s(s-c) = ab \Rightarrow \cos^2\frac{C}{2} = \frac{1}{4} \Rightarrow C = 120^\circ$. Then $R = \frac{c}{\sqrt{3}}$.
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