A circle is folded
over so that the
folded minor touches diameter AC
of the original circle at point B. If
AC = 8, AB :BC = 3:1, find the
exact length of chord DE.
Answers
Given : A circle is folded over so that the folded minor touches diameter AC of the original circle at point B. If AC = 8, AB :BC = 3:1,
To find : exact length of chord DE.
Solution:
AC = 8
AB : BC = 3 : 1
=> AB = (3/(3 + 1)) * 8 = 6
BC = 2
Let say O is the center of circle
Then OB = (8/2) - 2 = 2
Original distance of point ( lat say X) at circle touching now point B
= Radius of circle = 4
=> OX = 4
OB = 4
=> BX = √4² - 2² = 2√2
DE will intersect BX , let say at Y
=> BY = XY = 2√2/2 =√2
Let say M is the mid point of DE
DM² = OD² - OM²
OD = Radius = 4
OM = BY = √2
=> DM² = 4² - (√2)²
=> DM² = 16 - 2
=> DM² = 14
=> DM = √14
DE = 2 DM
=> DE = 2√14
2√14 is the length of chord DE
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