Thread: locus

a variable circle passes thrpugh a fixed point and cuts a fixed circle at the ends of a variable diameter of the fixed circle. Show that the locus of the centre of the variable circle is a straight line.

i have drawn various diagrams, to test my hypothesis that this is a straight line perpendicular to the line going the fixed point and the centre of the fixed circle, it seems to be correct, however i can produce no prove what so ever of this case, can ny one help plz,

i also need to prove the converse, ie, if centre of variable circle lies on this locus, then the variable circle cuts the fixed circle such that the line joining the intersection points passes through the cetre of the fixed circle

Originally Posted by calculus_jy

a variable circle passes thrpugh a fixed point and cuts a fixed circle at the ends of a variable diameter of the fixed circle. Show that the locus of the centre of the variable circle is a straight line.

i have drawn various diagrams, to test my hypothesis that this is a straight line perpendicular to the line going the fixed point and the centre of the fixed circle, it seems to be correct, however i can produce no prove what so ever of this case, can ny one help plz,

i also need to prove the converse, ie, if centre of variable circle lies on this locus, then the variable circle cuts the fixed circle such that the line joining the intersection points passes through the cetre of the fixed circle

I'm not quite sure but maybe these sites help a little bit further:

Apollonian_Circles

Lemoine Axis -- from Wolfram MathWorld