Question
Download Solution PDFThe 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.]
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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:
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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