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))`

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)

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.

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)

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+ b+c + d = 4 then the value of 1/((1-a) (1-b) (1-c)) + 1/((1-b) (1-c) (1-d)) + 1/((1-c)(1-d)(1-a)) + 1/((1-d)(1-a) (1-b)) is

Find the value of p for which the line through the points A(4,1,2) and B(5,p,0) is perpendicular to the line through the points C(2,1,1) and D(3,3,-1) .

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))