Question
Download Solution PDFTwo circles of radii 30 cm and 40 cm intersect each other, and the length of their common chord is 48 cm. What is the distance (in cm) between their centers?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
r = 30 cm
R = 40 cm
Length of Common Chord = 48 cm
Calculation:
XZ2 = XA2 – ZA2
⇒ XZ2 = 302 – 242
⇒ XZ2 = 900 – 576
⇒ XZ2 = 324
⇒ XZ = √324
⇒ XZ = 18 cm
YZ2 = YA2 – AZ2
⇒ YZ2 = 402 – 242
⇒ YZ2 = 1600 – 576
⇒ YZ2 = 1024
⇒ YZ = √1024
⇒ YZ = 32 cm
∴ The distance between the centres of circles = (18 + 32) = 50cm
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