Question

The difference of the radii of the two circles with centre (4,3) and touching the circle x^2+y^2=1 , is
1. 0
2. 2
3. 4
4. Not fixed

Answer 1

Answer:

sorry I don't know the answer

Answer 2

Step-by-step explanation:

center of bigger semicircle(radius=3) is R1

,the next bigger one (radius=2) is R2

and the smaller one(radius=1) is R3

and complete circle one is R (assume its radius is r )

Now consider the triangle R2R3R and draw a line from RtoR1 it acts as a cevian on this triangle lengths of triangle

R2R3=3

R2R=2+R

R3R=1+R

R1R=3−R [bigger circle is normal and complete circle are same so radius of both coincide]

R2R1=1

R3R1=2

now apply cosine rule at point R1

2×1×(3−r)

(2+r)2−12−(3−r)

2

=

2×2×(3−r)]

−[(1+r)2−22−(3−r)

2

solving this we get r=

14

12

=

7

6

p+q=13