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Two different non-parallel lines cut the...

Two different non-parallel lines cut the circle `|z| = r` at points `a, b, c and d`, respectively. Prove that these lines meet at the point given by `(a^-1+b^-1-c^-1-d^-1)/(a^-1b^-1-c^-1d^-1)`

A

`(a^(-1) + b^(-1) + c^(-1) + d^(-1))/(a^(-1)b^(-1)+c^(-1)d^(-1))`

B

`(ab+cd)/(a+b+c+d)`

C

`(a^(-1)+b^(-1)-c^(-1)-d^(-1))/(a^(-1)b^(-1)-c^(-1)d^(-1))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
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Two different non-parallel lines cut the circle |z|=r at points a,b,c and d, respectively. Prove that these lines meet at the point given by (a^(-1)+b^(-1)-c^(-1)-d^(-1))/(a^(-1)b^(-1)-c^(-1)d^(-1))

Two different non parallel lines cut the circle |z|=r at points a;b;c;d respectively.prove that these lines meet at a point ((a^(-1)+(b^(-1)-c^(-1)-d^(-1))/(a^(-1)b^(-1)-c^(-1)d^(-1))

Knowledge Check

  • If a, b, c and d are four positive numbers such that a+b+c+d=4 , then what is the maximum value of (a+1)(b+1)(c+1)(d+1) ?

    A
    32
    B
    8
    C
    16
    D
    81

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