The length of the common chord of two circles of radii 18 cm and 16 cm is 19.2 cm. What is the distance between the centres of the two circles? [Give your answer correct to the nearest integer value.]

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  1. 23 cm
  2. 28 cm
  3. 20 cm
  4. 35 cm

Answer (Detailed Solution Below)

Option 2 : 28 cm
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Detailed Solution

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Given:

The length of the common chord of two circles of radii 18 cm and 16 cm is 19.2 cm.

Concept used:

1. The line of centres of two intersecting circles perpendicularly bisects their common chord.

2. In a right-angled triangle, Height2 + Base2 = Hypotenuse2

Calculation:

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Let, P and Q be the centres of the larger and smaller circles respectively.

So, PA = 18 cm, QA = 16 cm.

AB is the common chord. So, AB = 19.2 cm

According to the concept,

PQ perpendicularly bisects AB at D. So, AD = DB = 19.2/2 = 9.6 cm

Considering ΔADQ,

AD2 + DQ2 = QA2

⇒ DQ2 = 162 - 9.62

⇒ DQ2 = 163.84

⇒ DQ = 12.8

Considering ΔADP,

AD2 + DP2 = PA2

⇒ DP2 = 182 - 9.62

⇒ DP2 = 231.84

⇒ DP ≈ 15.2

Hence, PQ = DQ + DP = 12.8 + 15.2 = 28

∴ The distance between the centres of the two circles is 28 cm.

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