In the attached figure O is the center of the circle AB=x and BP = 1,Prove that PB represents the square root of x. (NO absurd and useless answers please)
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Given : O is the center of the circle AB=x and BP = 1,
To Find : Prove that PB represents the square root of x.
Solution:
OA = OP = OC = radius
AB = x
AC = AB + BC = x + 1
AC = Diameter = 2 * Radius
=> Radius = (x + 1)/2
=> OA = OP = OC = (x + 1)/2
PB = OC - BC = (x + 1)/2 - 1 = (x - 1)/2
PB² = OP² - OB²
=> PB² = {(x + 1)/2}² - {(x - 1)/2}²
using a² - b² = (a + b)(a - b)
=> PB² = (x )(1)
=> PB = √x
QED
Hence proved
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