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 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 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))

If a,b,c,d be four distinct positive quantities in GP,then (a) a+dgtb+c (b) c^(-1)d^(-1)+a^(-1)b^(-1)gt2(b^(-1)d^(-1)+a^(-1)c^(-1)-a^(-1)d^(-1))

Three points represented by the complex numbers a,b,c lie on a circle with centre 0 and rdius r. The tangent at C cuts the chord joining the points a,b and z. Show that z= (a^-1+b^-1-2c^-1)/(a^-1b^1-c^2)

For non-singular square matrix A ,\ B\ a n d\ C of the same order (A B^(-1)C)^(-1)= A^(-1)B C^(-1) (b) C^(-1)B^(-1)A^(-1) (c) C B A^(-1) (d) C^(-1)\ B\ A^(-1)

If PA;PB;PC and PD are parallel to a line 1 then points P;A;B;C and D are collinear.

If PA;PB;PC and PD are parallel to a line 1 then points P;A;B;C and D are collinear.

Show that the line joining the points A(4,8) and B(5,5) is parallel to the line joining the points C(2,4) and D(1,7).

If a and b are the intercepts made by the straight line on the coordinate axes such that (1)/(a)+(1)/(b)=(1)/(c) then the line passes through point (A) (1,1) (B) (c,c) (C) ((1)/(c),(1)/(c))

What is the reflection of the point (-3,1) in the line x =-2? (A) (-1,1) (B) (-3,-5) (c ) (1,1) (D) - 3,5)

The sum of the reciprocals of the intercepts of a line is (1)/(2) , then the line passes through the point is "________" . (a) (1, 1) " " (b) (2,1) " " (c) ((1)/(4) , (1)/(4)) (d) (2,2)