Question

find the locus of centres of circles which touch two intersecting lines

Answer 1

Let l1 and l2 be two intersecting lines. Suppose a circle with centre O touches the lines l1 and l2 at M and N respectively.

∴ OM = ON (Radius of the same circle)

⇒ O is equidistant form l1 and l2.

Similarly, centres of any other circle which touches the intersecting lines l1 and l2 will be equidistant from l1and l2.

Now, ΔOPM ΔOPN (RHS congruence criterion)

∴ ∠MPO = ∠NPO

⇒ O lies on the bisector of the angles between l1 and l2 i.e., O lies on l.

Thus, the locus of centres of circles which touches two intersecting lines is the angle bisector between the two lines.

Answer 2

here is your answer......