X and Y are two points on the circumference of a circle having a diameter of 20 cm. The length of the line segment XY is 16 cm. Find the distance (in cm) of the line segment XY from the center of the circle.
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Correct answer: A
Explanation
The correct answer is option 1 i.e. 6.
Given,
length of the line segment XY is 16 cm
Radius (r) = Diameter/2 = 20/2 = 10 cm
Now, Let d be the distance of the line segment XY from the center of the circle.
According to the question;
Using the Pythagorean theorem,
⇒ r2 = (XY/2)2 + d2
⇒ 102 = (16/2)2 + d2
⇒ 100 - 64 = d2
⇒ d2 = 36
⇒ d = 6