Question

if 2spheres of radius 3cm and 4cm cut orthogonally find the radius of the common circle

Answer 1

Answer:

correct answer

Step-by-step explanation:

Let L be the length of the common chord.

Given. two circles of radii 3, 4 intersect orthogonally.

So, ∠Q=90

0

∴(C

1

C

2

)=

3

2

+4

2

Taking square of both sides.

∴(C

1

C

2

)

2

=3

2

+4

2

∴(C

1

C

2

)=5

∴(ΔAC

1

C

2

)=

2

1

×4×3=6...(1)

Step 2: Find chord length.

Also AB is perpendicular to C

1

C

2

.

Area of (ΔAC

1

C

2

)=

2

1

×C

1

C

2

×

2

L

=

4

1

×5×L...(2)

From (1) and (2)

⇒

4

5L

=6

⇒L=

5

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