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1. Two concentric circles of radii a and b(a > b) are given. Find the length of the chord of the larger circle which touches the smaller circle.
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Answer:
Let AB be chord of larger circle which touches smaller circle
So, AB becomes tangent to Smaller circle
As we know ,Perpendicular drawn from centre bisects the chord
So, Draw perpendicular from O to AB
Let foot of perpendicular be D
So, AD =DB
And As AB is tangent to smaller circle
So, OD becomes normal
So, OD = radius of smaller circle = b
OA = radius of larger circle = a
In ∆OAD,
OA^2 = OD^2 + AD^2
AD^2 = OA^2 - OD^2
= a^2 - b^2
AD= √(a^2-b^2)
SO, AB = 2×AD
= 2√(a^2-b^2)
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