# Geo4.68

From Example Problems

Tangents are drawn to the circle from a point which always lies on the line .Prove that the locus of the mid-point of the chords of contact is .

Given circle is

Let this be 1.

Given line is

Let this equation be 2.

Let (h,k) be a point on the line 2, hence .

This is equation 3

The equation of the chord of contact of tangents from (h,k)to the circle is

Let this be equation 4

Let (x1,y1) be the mid point of the chord, then teh equation of the chord is

Le this be 5.

The equations 4 and 5 represent the same.

Hence

Therefore

Substituting these values in the equation 3, we get

Hence the locus of (x1,y1) is