Question

If the length of diameters of two concentric circles are 17 cm and 15 cm, then the length of the chord of the circle which is tangent to the inner circle is

• A.
  4 cm
• B.
  8cm
• C.
  12 cm
• D.
  16 cm

Answer 1

The correct option is B

8cm
Let O be the centre of two concentric circles. Since, diameters of 2 concentric circles are 17 cm and 15 cm

$\therefore AO=\frac{17}{2}cmandOC=\frac{15}{2}cm$


AB is the chord to the outer circle and tangent to the inner circle.

$\therefore OC\perp AB$
(Angle between a tangent and the radius of a circle is 90°)

In $\Delta$OCA,
By Pythagoras theorem,

$O{A}^2=O{C}^2+A{C}^2\Rightarrow A{C}^2={\left(\frac{17}{2}\right)}^2-{\left(\frac{15}{3}\right)}^2\Rightarrow A{C}^2=\frac{289-225}{4}=16\Rightarrow AC=4cm$

Since, the perpendicular from the centre to a chord bisects the chord.

$\therefore AB=2AC=8cm$

Hence, the correct answer is option b.