Circle And System Of Circles Question 252
Question: The lengths of tangents from a fixed point to three circles of coaxial system are $ t_1,t_2,t_3 $ and if P, Q and R be the centres, then $ QRt_1^{2}+RPt_2^{2}+PQt_3^{2} $ is equal to
Options:
A) 1
B) 2
C) 3
D) 0
Show Answer
Answer:
Correct Answer: D
Solution:
Co-axial system $ x^{2}+y^{2}+2gx+c=0 $ , (g variable)
L.H.S. = $ \Sigma (g_2-g_3)(h^{2}+k^{2}-c+2g_1h)=0 $
Since $ \Sigma (g_2-g_3)=0 $ and $ \Sigma g_1(g_2-g_3)=0 $ .
BETA
