Out of the 2 concentric circle the radius of the outer circle is 5 cm and the chord AC of the length 8 cm is a tangent to the inner circle find the radius of the inner circle

Options

A. 2 cm
B. 3 cm
C. 4 cm
D. 5 cm

Answer

B

Explanation

Let `C_(1)` and `C_(2)` be the two circles having same centre O. AC is a chord which touches the `C_(1)` at point D.

Join OD.
Also, `ODbotAC` `:.AD=DC=4cm` [perpendicular line OD bisects the chord]
In right angled `DeltaAOD,` `OA^(2)=AD^(2)+DO^(2)`
`["by Pythagoras theroem",i.e.,("hypotenuse")^(2)=("base")^(2)+("perpendicu lar")^(2)]`
`rArrDO^(2)=5^(2)-4^(2)`
`=25-16=9`
`rArrDO=3cm`
:. Radius of the inner circle OD=3cm.