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Question

If A(2ca,cb),B(ca,0) and C(1+ca,1b) are three points, then

A
(AB)2+(BC)2(CA)2=2c
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B
(AB)2+(BC)2(CA)2=c2+1(c1)2
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C
(AB)2+(BC)2(CA)2=2c(a2+b2)a2b2
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D
(AB)2(BC)2(CA)2=2b
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Solution

The correct options are
B (AB)2+(BC)2(CA)2=c2+1(c1)2
C (AB)2+(BC)2(CA)2=2c(a2+b2)a2b2
As A(2ca,cb),B(ca,0) and C(1+ca,1b)
AB=(ca2ca)2+(0cb)2=c2a2+c2b2BC=(1+caca)2+(1b0)2=1a2+1b2AC=(1+ca2ca)2+(1bcb)2=(1aca)2+(1bcb)2
Hence,
(AB)2+(BC)2(AC)2=c2a2+c2b2+1a2+1b2(1aca)2+(1bcb)2=c2+1(c1)2(AB)2+(BC)2(AC)2=c2a2+c2b2+1a2+1b2(1aca)2(1bcb)2=2c(a2+b2)a2b2

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