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 `z=(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 AP, then (a) bcgtad (b) c^(-1)d^(-1)+a^(-1)b^(-1)gt2(b^(-1)d^(-1)+a^(-1)c^(-1)-a^(-1)d^(-1))

Two different non-parallel lines meet the circle abs(z)=r . One of them at points a and b and the other which is tangent to the circle at c. Show that the point of intersection of two lines is (2c^(-1)-a^(-1)-b^(-1))/(c^(-2)-a^(-1)b^(-1)) .

Two systems of rectangular axis have the same origin. If a plane cuts them at distances a, b, c and a', b', c', respectively from the origin, then prove that (1)/(a^2)+(1)/(b^2)+(1)/(c^2)=(1)/((a')^2)+(1)/((b')^2)+(1)/((c')^2) .

Prove the followings : "cot"^(-1)(ab+1)/(a-b)+"cot"^(-1)(bc+1)/(b-c)+"cos"^(-1)(ca+1)/(c-a)=pi(agtbgtc)

Prove that the lines x=2 (y-1)/(3) = (z-2)/(1) and x = (y-1)/(1) = (z+1)/(3) are skew lines.

Prove that : cot^(-1)((1+ab)/(a-b))+cot^(-1)((1+bc)/(b-c))+cot^(-1)((1+ca)/(c-a))=pi,(a>b>c>0)

Prove that the line through the point (x_1, y_1) and parallel to the line Ax + By + C=0 is A(x-x_1) + B(y-y_1)=0 .

If a, b, c are in A.P., b, c, d are in G.P. and 1/c,1/d,1/e are in A.P. prove that a,c,e are in GP.

(x^(1/(a-b)))^(1/(a-c))xx(x^(1/(b-c)))^(1/(b-a))xx(x^(1/(c-a)))^(1/(c-b))

If a,b,c are in geometric progression then ((1)/(b)+ (1)/(c )-(1)/(a)) ((1)/(c ) + (1)/(a) - (1)/(b)) = ……..