Question

In the given figure ab = 30 and cd =24. What is the value of MN .
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Answer 1

Given

• AB = 30 cm
• CD = 24 cm

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To Find

• The value of MN

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Solution

Method 1

AB = 30 cm

CD = 24 cm

MN = (30 - 24) + 24 ÷ 2

Using BODMAS we will find the answer.

⇒ (30 - 24) + 24 ÷ 2

⇒ 6 + 24 ÷ 2

⇒ 6 + 12

⇒ 18

∴ The value of MN (in cm) is 18.

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Method 2

We'll find the value of AC and DB and accordingly we will solve.

So AC = DB

⇒ (30 - 24) ÷ 2

⇒ 6 ÷ 2

⇒ 3 cm

∴ The value of AC and DB is 3 cm respectively.

The center of the circle is 9 cm (3 × 3).

So we will multiply '2' to 9 to find the value of MN (This is because AC = DB so we need to either add 9+9 or multiply 2 to 9 to find the value of MN).

9 × 2 = 18

∴ The value of MN (in cm) is 18.

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Answer 2

question:

In the given figure, AB = 30 cm and CD = 24 cm. What is the value (in cm) of MN?

solution:

18

Given:

• figure.
• AB = 30
• CD = 24

To find:

the value of MN?

step by step explanation:

given , CD = 24

so , let's find AC and DB

30 - 24 = 6 ÷ 2 = 3 ( Given , AB = 30 )

∴ AC , DB = 3 cm

To find MN we need to:

$\sf radius \: of \: inner \: circle = \frac{24}{2} = 12cm$

$\sf radius \: of \: outer \: circle = \frac{30}{2} = 15cm$

according to pythagorean triplet :

as we know 9,12,15 is Pythagorean triplet.

so , till the center of the two circles it is 9cm

thus , 9 × 9 = 18cm

therefore,

MN = 18cm