Question
Download Solution PDFA is the centre of circle with radius 8 cm and B is the centre of circle whose diameter is 8 cm. If these two circles touch externally, then find the area of the circle with diameter AB
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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Circle 1: Center A, Radius = 8 cm
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Circle 2: Center B, Diameter = 8 cm ⇒ Radius = 4 cm
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The two circles touch externally.
Concept Used:
The distance between the centers of two circles that touch externally is equal to the sum of their radii.
Formula for the area of a circle: Area = π × (radius)2
Calculation:
Distance between centers A and B = Radius of Circle 1 + Radius of Circle 2
⇒ AB = 8 cm + 4 cm = 12 cm
Diameter of the circle with AB as its diameter = 12 cm
Radius of the circle = Diameter / 2 = 12 / 2 = 6 cm
Area of the circle = π × (radius)2
⇒ Area = π × 62
⇒ Area = π × 36
∴ Area of the circle = 36 π cm2
Last updated on Jul 1, 2025
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