Question

hii...pls...ans and explain also

Answer 1

Answer is

(3) 6cm

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Answer 2

Answer:

6 cm

Step-by-step explanation:

Let us assume that OA = OB = 5 cm and O'A = O'B = 3 cm.

⇒ AC = CB

Given that OO' = 4 cm

Let OC = x. Then,O'C = x - 4

(i)

In ΔOAC,

⇒ OA² = AC² + OC²

⇒ 5² = AC² + x²

⇒ 25 = AC² + x²

⇒ 25 - x² = AC²

(ii)

In O'AC,

⇒ O'A² = AC² + O'C²

⇒ 3² = AC² + (x - 4)²

⇒ 9 = AC² + x² + 16 - 8x

⇒ AC² = -x² - 7 + 8x

On solving (i) & (ii),we get

⇒ 25 - x² = -x² - 7 + 8x

⇒ 25 - x² + x² + 7 - 8x = 0

⇒ 32 = 8x

⇒ x = 4.

Hence,the common chord will pass through O' and therefore it will be diameter of smaller circle.

⇒ AC² = 25 - x²

⇒ AC² = 25 - 4²

⇒ AC² = 25 - 16

⇒ AC² = 9

⇒ AC = 3 cm.

Length of common chord = 2AC = 2 * 3 cm = 6 cm.

Hope it helps!