Question

In the figure, $MNS$ is tangent to the circle with centre $O$ at $N$.

$AB$ is chord parallel to $MNS$. find $\angle ANC$

• A. ${50}^{\circ }$
• B. ${90}^{\circ }$
• C. ${40}^{\circ }$
• D. ${20}^{\circ }$

Answer 1

The correct option is C ${40}^{\circ }$

In $△ACN$ and $△BCN$,

$AC=BC$ ........[Perpendicular from center to chord, bisects chord].

$\angle NCB=\angle NCA={90}^{\circ }$ ........[given]

$NC=NC$ .......[common side]

$\therefore \Delta ACN\cong \Delta BCN$

$\therefore AN=BN$ .......[C. S. C. T.]

$\angle ANC=\angle CNB$ .......[C. A. C. T.]

But $\angle CNS={90}^{\circ }$

$\angle CNB+\angle BNS={90}^o$

$\angle CNB+{50}^o={90}^o$

$\angle CNB={40}^o=\angle ANC$