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Question:

Two circles of radii 18 cm and 16 cm intersect each other and the length of their common chord is 20 cm. What is the distance (in cm) between their centres?

Explanation:

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From triangle AGH,

AH² + GH² = AG²

AH² + 10² = 16²

AH² + 100 = 256

AH² = 156

AH = 2$\sqrt{39}$

From triangle CGH,

CH² + GH² = CG²

CH² + 10² = 18²

CH² + 100 - 324

CH² = 224

CH = 4$\sqrt{14}$

Distance between centres of circles = AC = AH + CH = 2$\sqrt{39}$ + 4$\sqrt{14}$

Hence, the correct answer is Option D