Question
Download Solution PDFTwo circles having equal radius intersect each other such that each passes through the center of the other. Sum of diameter of these two circles is 84 cm. What is the length of the common chord?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Sum of diameter of these two circles is 84 cm
Calculation:
Diameter of one circle = 84/2 = 42 cm
Radius of the circle = 42/2 = 21 cm
According to the diagram,
AD = DB
O1O2 = 21
Again O1A = O2A = 21 [Radius of the circle]
∠ADO1 = 90°
O1D = O2D = 21/2
AD = √(441 - 441/4)
⇒ 21√3/2
AB = 2 × 21√3/2 = 21√3
∴ The length of the common chord is 21√3 cm
Last updated on May 28, 2025
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