Question

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XY is a tangent to two circles of radii 12cm and 4 cm respectively.If the circles touch each other Find the area of the region bounded by the circles and tangents.

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Answer 1

Answer:

Solution

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Correct option is A)

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

Hence, the given statement is true.

Answer 2

Answer:

So here is your answer

Construct EC// AB

AB= 15 cm=EC

AD=12cm

CB=4cm

DE=12-4=8cm

(Tangent is perpendicular to radius)

ABCD is rectangle and DEC is a right-angle triangle

SO,

DC²=EC²+DE²

DC=12cm

Step-by-step explanation:

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