Question

In the given figure, O is the centre of the circle $C_1$. If CD and CB are the tangents to the circle $C_1$ at point D and B respectively, then $\angle BDC$ is equal to

• A.
  ${70}^{\circ }$
• B.
  ${60}^{\circ }$
• C.
  ${50}^{\circ }$
  
• D.
  ${80}^{\circ }$

Answer 1

The correct option is C

${50}^{\circ }$

Given that, $\angle BCD={80}^{\circ }$and CD and CB are tangents of C_1.




$CB=CD$

We know that the angles opposite to equal sides are equal.
$\therefore \angle CBD=\angle BDC\dots ..\left(i\right)In\Delta BCD,Byanglesumproperty\angle BCD+\angle BDC+\angle CBD={180}^{\circ }\Rightarrow {80}^{\circ }+2\angle BDC={180}^{\circ }\left[From\right(i\left)\right]\Rightarrow 2\angle BDC={100}^{\circ }\Rightarrow \angle BDC={50}^{\circ }$

Hence, the correct answer is option c .