Question

xy is a tangent of two circles of radii 12cm and 4cm.if the circles touch each other find the area of region bounded by the circles and tangents​

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

Answer 2

• 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,

BE²+EA²=BA²

x²=8²+15²

x²=289

x=17 cm