Question 73

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?

Solution

From triangle AGH,

AH$$^2$$ + GH$$^2$$ = AG$$^2$$

AH$$^2$$ + 10$$^2$$ = 16$$^2$$

AH$$^2$$ + 100 = 256

AH$$^2$$ = 156

AH = $$2\sqrt{39}$$

From triangle CGH,

CH$$^2$$ + GH$$^2$$ = CG$$^2$$

CH$$^2$$ + 10$$^2$$ = 18$$^2$$

CH$$^2$$ + 100 = 324

CH$$^2$$ = 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

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