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.

Answer 1

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, OD is perpendicular to AC
$\therefore$ AD=DC=4 cm [ Perpendicular line OD bisects the chord]
In right angled,
$\Delta AOD,O{A}^2=A{D}^2+D{O}^2$
[By phthagoras theorem: ( hypotenuse)${}^2$ = (base)${}^2$ + ( perpendicular)${}^2$]
$\Rightarrow D{O}^2=5^2-4^2=25-16=9\Rightarrow DO=3cm$
$\therefore$ Radius of the inner circle = 3cm