Question

In the given figure, AB and CD are two equal chords of a circle. The angle ODC will be equal to

• A. ${60}^{\circ }$
• B. ${70}^{\circ }$
• C. ${55}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is C

${55}^{\circ }$

AB and CD are equal chords, so they will subtend an equal angle at the center.

So, $\angle AOB=\angle COD$

$\angle COD={70}^{\circ }$

Now $\Delta COD$ is isoceles triangle as OC = OD (radius)
$\therefore \angle OCD=\angle ODC$

In $\Delta COD$,

$\angle COD+\angle OCD+ODC={180}^{\circ }$

${70}^{\circ }+2\angle ODC={180}^{\circ }$

$\therefore \angle ODC=\frac{{180}^{\circ }-{70}^{\circ }}{2}={55}^{\circ }$