Area and Perimeter Practice Test 3

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Question : 13 of 40

Marks: +1, -0

Two circles touch externally. The sum of their areas is 130 π

cm^2

and the distance between their centres is 14 cm. Find the radii of the circles.

8 cm; 6 cm
9 cm; 5 cm
10 cm; 4 cm
11 cm; 3 cm

Solution:

Here,

r_1+r_2

= 14 cm ... (i)
And also,

πr_1^2+πr_2^2

= 130 π
⇒

r_1^2+r_2^2

= 130 ... (ii)
Now,

(r_1+r_2)^2

=

r_1^2+r_2^2+2r_1r_2

⇒

(14)^2

= 130 +

2r_1r_2

∴

r_1r_2

= 33
Then,

r_1-r_2

=

√{(r_1+r_2)^2-4r_1r_2}

=

√{(14)^2-4×33}

=

√{64}

= 8
Hence,

r_1

=

1/2

(4 + 8) = 11 cm

r-2

=

1/2

(14 - 8) = 3 cm

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