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Question 1
Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8cm is a tangent to the inner circle,. Find the radius of the inner circle.

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Solution

Let C1, and C2 be the two circles having same centre O.
AC is a chord which touches the C1 at point D.

Join OD.
Also, OD is perpendicular to AC
AD=DC=4 cm [ Perpendicular line OD bisects the chord]
In right angled,
ΔAOD, OA2=AD2+DO2
[By phthagoras theorem: ( hypotenuse)2 = (base)2 + ( perpendicular)2]
DO2=5242=2516=9DO=3cm
Radius of the inner circle = 3cm



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