Question 55

Two circles of radius 15 cm and 37 cm intersect each other at the points A and B. If the length of common chord is 24 cm, what is the distance (in cm) between the centres of the circles?

Solution

From triangle AHG,

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

AH$$^2$$ + 12$$^2$$ = 15$$^2$$

AH$$^2$$ + 144 = 225

AH$$^2$$ = 81

AH = 9 cm

From triangle CHG,

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

CH$$^2$$ + 12$$^2$$ = 37$$^2$$

CH$$^2$$ + 144 = 1369

CH$$^2$$ = 1225

CH = 35 cm

Distance between two circles = AC = AH + CH = 9 + 35 = 44 cm

Hence, the correct answer is Option A

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