Question

Two circles C1
and C2
of radius 2 and 3 respectively
touch each other as shown in the figure. If AD and
BD are tangents then the length of BD is
D
A B
C12 C23

Answer 1

Answer:

it answer will be C

1

(r,0)

C

2

(R,0)

Eq. of AB y=r

Eq. of circle C

2

(x−R)

2

+y

2

=R

2

A(R−

R

2

−r

2

,r) using R

2

=2r

2

B(R+

R

2

−r

2

,r)A(R−r,r),B(R+r,r)

Slope of OA=

R−r

r

=m

1

Slope of OB=

R+r

r

=m

2

tanθ=

1+m

1

m

2

m

1

−m

2

=1

θ=45

∘

.

Answer 2

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