Question

(prove that) If the polar of the points on the circle x2+y2=a2 with respect to the circle x2+y2=b2 touches the circle x2+y2=c2 then prove that a, b, c, are in Geometrical progression.

Answer 1

Answer:

no problem i'll tell it later on

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Letp(x1, y1) be a point onx2 + y2 = a2

i.e x21 + y21 = a2 → (1)

the equation of polar of(x1, y1) with respect to circlex2 +y2 = b2 is

xx1 + yy1 − b2 = 0

it touchesx2 + y2 = c2 thenr = d

c =  mod x1(0)+y1(0)-b2/root x square 1 +y square 1

c = mod -b/root a square

ac =b2

∴ a, b, c are in G.P