Question

In the given figure, the two concentric circles are centred at O. If BD = 2 cm, CD = 12 cm, then the radius of the larger circle is

• A.
  6 cm
• B.
  8 cm
• C.
  10 cm
• D.
  12 cm

Answer 1

The correct option is C

10 cm
Given that BD = 2 cm, CD = 12 cm and $OE\perp CD.$


In two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.

$\therefore OEbisectsthechordCD.\Rightarrow CE=ED=\frac{CD}{2}=6cm$
In$\Delta OED$, by Pythagoras theorem,

$O{D}^2=O{E}^2+E{D}^2\Rightarrow (OB+2{)}^2=O{B}^2+6^2(\therefore OB=OE=Radii)\Rightarrow O{B}^2+4+4OB=O{B}^2+36\Rightarrow 4OB=36–4=32\Rightarrow OB=8cm\therefore OD=OB+BD=8+2=10cm$

Thus, the radius of the larger circle, OD is 10 cm.

Hence, the correct answer is option c .