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Find out the Relation between C1, C2, C3...

Find out the Relation between `C_1, C_2, C_3 and C_4` such that point A and B are equipotential. [Balanced wheat stone bridge]

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If a + 2b + 3c = 0 " then " a/3+(2b)/3+c=0 and comparing with line ax + by + c, we get x = 1/3 & y = 2/ 3 so there will be a point (1/3,2/3) from where each of the lines of the form ax + by + c = 0 will pass for the given relation between a,b,c . We can say if there exists a linear relation between a,b,c then the family of straight lines of the form of ax + by +c pass through a fixed point . If a , b,c are in A.P., then the line ax + 2by + c = 0 passes through

If a + 2b + 3c = 0 " then " a/3+(2b)/3+c=0 and comparing with line ax + by + c, we get x = 1/3 & y = 2/ 3 so there will be a point (1/3,2/3) from where each of the lines of the form ax + by + c = 0 will pass for the given relation between a,b,c . We can say if there exists a linear relation between a,b,c then the family of straight lines of the form of ax + by +c pass through a fixed point . If a , b,c are in A.P., then the line ax + 2by + c = 0 passes through

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If a point C lies between two points A and B such that A C=B C , then prove that A C=1/2A B . Explain by drawing the figure.