Chord of the Bigger Circle Is Bisected at the Point of Contact with the Smaller Circle
Question 1Out...
Question
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=52−42=25−16=9⇒DO=3cm ∴ Radius of the inner circle = 3cm