Circle And System Of Circles Question 253

Question: P, Q and R are the centres and $ r_1,r_2,r_3 $ are the radii respectively of three co-axial circles, then $ QRr_1^{2}+RP,r_2^{2}+PQr_3^{2} $ is equal to

Options:

A) $ PQ\ .,QR,.,RP $

B) $ -PQ,.,QR,.,RP $

C) $ PQ^{2}.QR^{2}.RP^{2} $

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

As $ \Sigma g_1^{2}(g_2-g_3)=-(g_1-g_2)(g_2-g_3)(g_3-g_1) $ .