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In the diagram, the two circles have a common centre O. If the area of the large...


Question

In the diagram, the two circles have a common centre O. If the area of the larger circle is 100\(\pi\) and that of the smaller circle is 49\(\pi\), find x

Options

A) 2

B) 3

C) 4

D) 6

The correct answer is B.

Explanation:

area of larger circle = 100\(\pi\)

\(\pi r^2 = 100\pi\)

R2 = 100

R = 10(Radius)

Area of smaller circle = \(49 \pi\)

\(\pi r^2 = 49\pi\)

r2 = 49

r = 7(radius)

Since R = x + r

x = R - r

x = 10 - 7 = 3


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Dicussion (1)

  • area of larger circle = 100\(\pi\)

    \(\pi r^2 = 100\pi\)

    R2 = 100

    R = 10(Radius)

    Area of smaller circle = \(49 \pi\)

    \(\pi r^2 = 49\pi\)

    r2 = 49

    r = 7(radius)

    Since R = x + r

    x = R - r

    x = 10 - 7 = 3

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