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))`.

Draw a circle and two lines parallel to a given line such that one is tangent and the other, a secant to the circle.

Two circles intersect at two points A and B AD and AC are diameters to the two circles Prove that B lies on the line segment DC.

If the line lx + my = 1 is a tangent to the circle x^(2) + y^(2) = a^(2) , then the point (l,m) lies on a circle.

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))

Show that the two lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-4)/5=(y-1)/2=z intersect. Find also the point of intersection of these lines.

Fill in the blanks Draw a circle and two lines parallel to a given line drawn outside the circle such that one is a tangent and the other, a secant to the circle.

Two equal circle touch each other externally at C and AB is a common tangent to the circle. Then. angleACB=……. .

There are n straight lines in a plane such that n_(1) of them are parallel in onne direction, n_(2) are parallel in different direction and so on, n_(k) are parallel in another direction such that n_(1)+n_(2)+ . .+n_(k)=n . Also, no three of the given lines meet at a point. prove that the total number of points of intersection is (1)/(2){n^(2)-sum_(r=1)^(k)n_(r)^(2)} .

In the given figure, two circles with centres A and B touch each other at C bisects the common tangent at P and Q.

The perpendicular from the origin to the line y=mx+c meets it at the point (-1,2) . Find the values of m and c.