Circle And System Of Circles Question 232
Question: The length of the common chord of the circles $ {{(x-a)}^{2}}+{{(y-b)}^{2}}=c^{2} $ and $ {{(x-b)}^{2}}+{{(y-a)}^{2}}=c^{2} $ , is
Options:
A) $ \sqrt{4c^{2}-2{{(a-b)}^{2}}} $
B) $ \sqrt{4c^{2}+2{{(a-b)}^{2}}} $
C) $ \sqrt{4c^{2}-2{{(a+b)}^{2}}} $
D) $ \sqrt{4c^{2}+2{{(a+b)}^{2}}} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ C_1(a,\ b),\ C_2(b,\ a),\ r_1=r_2=c $
$ \therefore $ $ C_1P=\frac{1}{2}\sqrt{a^{2}+b^{2}+a^{2}+b^{2}-4ab} $
Length of common chord $ =2{{[ c^{2}-\frac{1}{4}{ 2(a^{2}+b^{2})-4ab } ]}^{1/2}} $
$ =2{{( \frac{2c^{2}-a^{2}-b^{2}+2ab}{2} )}^{1/2}}=\sqrt{4c^{2}-2{{(a-b)}^{2}}} $ .
BETA
