Question

Two circles of radii 5.5 cm and 2.2cm respectively touch each other internally. what is the distance between their centers A4.4cm B) 8.8cm C) 2.2 cm D) 8.8 or 2.2cm​

Answer 1

Answer:

We have

AB=5.6cm,AD=1.4cm,AC=7.2cm and AE=1.8cm.

∴ BD=AB−AD=(5.6−1.4) cm = 4.2 cm

and ,

EC=AC−AE=(7.2−1.8)cm = 5.4cm

Now,

DB

AD

=

4.2

1.4

=

3

1

and

EC

AE

=

5.4

1.8

=

3

1

⇒

DB

AD

=

EC

AE

Thus, DE divides sides AB and AC of △ABC in the same ratio.

Therefore, by the converse of Basic Proportionality Theorem, we have DE∣∣BC