Question
Download Solution PDFX and Y are two points on the circumference of a circle having diameter 20 cm. The length of the line segment XY is 16 cm. Find the distance (in cm) of the line segment XY from the centre of the circle.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
X and Y are two points on the circumference of a circle having diameter 20 cm.
The length of the line segment XY is 16 cm.
Formula used:
Using the Pythagorean theorem in a right triangle formed by the radius, the perpendicular distance from the center to the chord, and half the chord length.
Let d be the distance of the line segment XY from the center of the circle.
Radius (r) = 10 cm (since diameter = 20 cm)
Calculations:
Using the Pythagorean theorem:
\(r^2 = (\frac{XY}{2})^2 + d^2\)
r = 10 cm
XY = 16 cm
⇒ \(10^2 = (\frac{16}{2})^2 + d^2\)
⇒ \(100 = 8^2 + d^2\)
⇒ \(100 = 64 + d^2\)
⇒ \(d^2 = 36\)
⇒ \(d = \sqrt{36}\)
⇒ d = 6 cm
∴ The correct answer is option 2.
Last updated on Jun 26, 2025
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