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
A.
B.
C.
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 =
Create a free account to view solution
View Solution FreeMore Properties of Triangle Questions
The diameter of the circumcircle of a triangle with sides 5 cm, 6 cm and 7 cm is -...In a triangle PQR, ∠R = . If tan and tan are the roots of ax2 + bx + c = 0, a ≠ 0 then...Among the statements(S1) : If $A(5, - 1)$ and $B( - 2,3)$ are two vertices of a triangle, whose orthocentre is $(0,0)$, ...If in a triangle the angles are in A.P. and b : c = √3 : √2, then ∠A is equal to -...Let PS be the median of the triangle with vertices P(2, 2), Q(6, - 1) and R (7, 3). The equation of the line passing thr...