JEE Advanced | 2014Properties of TriangleHard
Question
In a triangle the sum of two sides is x and the product of the same two sides is y. If x2 - c2 = y, where c is the third side of the triangle, then the ratio of the in radius to the circum-radius of the triangle is
Options
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D.
Solution
a + b = x, ab = y, x2 - c2 = y
Now, (a + b)2 - c2 = ab
a2 + b2 - c2 = - ab
⇒ cos c = -
⇒ ∠c = 120o
2R =
⇒ R = 
r = (s - c). tan
r =
. √3
r =
Now, (a + b)2 - c2 = ab
a2 + b2 - c2 = - ab
⇒ cos c = -
⇒ ∠c = 120o2R =
⇒ R = r = (s - c). tan
r =
. √3r =
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