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Two equal circles pass through their centers. If radius of every circle is 5 cm. Which of the statements is correct? A. The length of common chord is equal to 5√3 cm B. Distance between the centers of two circle is equal to radius.

Two equal circles pass through their centers. If radius of every circle is 5 cm. Which of the statements is correct? A. The length of common chord is equal to 5√3 cm B. Distance between the centers of two circle is equal to radius. Correct Answer Both A and B

GIVEN:

Radius of every circle is 5 cm.

CONCEPT:

The common chord will divide the line AB into 2 equal parts.

CALCULATION:

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In the figure:

A and B are the centers of 2 circles.

⇒ AB = 5 cm (Radius)

The common chord will divide the line AB into 2 equal parts;

⇒ AO = OB = 5/2 cm

AC = 5 cm (Radius)

Applying Pythagoras theorem:

OC2 = AC2 – OA2

⇒ OC2 = 52 – (5/2)2

⇒ OC2 = 25 – 25/4 = 75/4

⇒ OC = 5√3/2 cm

Common chord CD = 2 × OC = 5√3 cm

∴ Both A and B are correct.

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