Home
Class 12
MATHS
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 `z` given by `(a^-1+b^-1-c^-1-d^-1)/(a^-1b^-1-c^-1d^-1)`

Promotional Banner

Similar Questions

Explore conceptually related problems

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))

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))

If a,b,c and d are four positive real numbers such that abcd=1 , what is the minimum value of (1+a)(1+b)(1+c)(1+d) .

If a line intersects two concentric circles ( circles with the same centre ) with centre O at A, B, C and D, prove that AB = CD.

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.

Two circle intersect at two points B and C. Through B, Two lines segment ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively. Prove that ACP = QCD .

Prove that the points A(1,-3),B(-3,0)and C(4,1) are the vertices of a right isosceles triangle .

The two lines x=ay+b, z=cy+d and x=a'y+b', z=c'y+d' are perpendicular to each other if :

Show that the points A(1,3),B(2,6),C(5,7) and D(4,4) are the vertices of a rhombus .