Arun
Last Activity: 7 Years ago
R^2 = P^2 + Q^2 + 2PQ cosθ ... ( 1 )
4R^2 = P^2 + 4Q^2 + 4PQ cosθ ... ( 2 )
4R^2 = P^2 + Q^2 - 2PQ cosθ ... ( 3 )
Multiplying eqn. ( 1 ) by 2 and subtracting from eqn. ( 2 ),
2R^2 = 2Q^2 - P^2 ... ( 4 )
Adding eqns. ( 1 ) and ( 3 ),
5R^2 = 2Q^2 + 2P^2 ... ( 5 )
Subtracting eqn. ( 4 ) from eqn. ( 5 ),
3R^2 = 3P^2 => P^2 = R^2
Plugging R^2 = P^2 in eqn. ( 4 ),
2P^2 = 2Q^2 - P^2
=> Q^2 = (3/2)P^2
=> P^2 : Q^2 : R^2 = P^2 : (3/2)P^2 : P^2
=> P : Q : R = √2 : √3 : √2.
