Question

If radii of two concentric circles are 13 cm and 5 cm, then the length of each chord of one circle which touches the other circle is

• A.
  6 cm
• B.
  12 cm
• C.
  24 cm
• D.
  36 cm

Answer 1

The correct option is C

24 cm
Let O be the centre of two concentric circles. AB be the chord of the bigger circle that is tangent to the inner circle.



$In\Delta ACO,\text{Apply pthagoras theroem,}\Rightarrow A{O}^2=O{C}^2+A{C}^2\Rightarrow {13}^2=5^2+A{C}^2\Rightarrow AC=\sqrt{169-25}\Rightarrow AC=12cm$

The perpendicular from the centre of a circle to a chord bisects the chord. Thus, OC bisects AB.

$\Rightarrow AB=2AC=24cm$

Hence, the correct answer is option c.