Question

AB is one of the direct common tangent of two circles of radii 12cm and 4cm respectively touching each other. find the area if the region enclosed by the circles and the tangent​

Answer 1

Answer:

Consider two circles of radii 12cm and 4cm with centers B and A respectively.

The length of direct common tangent to both the circles is 15cm.

CD=15 cm

CD=BE=15 cm

AE=AC−CE

AE=12−4=8 cm

AB=x cm

In the right triangle BEA,

Using Pythagoras theorem,

BE

2

+EA

2

=BA

2

x

2

=8

2

+15

2

x

2

=289

x=17 cm