Question

In the given figure, AB is a diameter and AC is a chord of the circle and the tangent at C intersects AB produced in D. If $\angle BAC={30}^{\circ }$, then $\angle ACD=$ ______.

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${100}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is D

${120}^{\circ }$

$\angle ACB={90}^{\circ }$ (angles in the semicircle)
$\angle BCD={30}^{\circ }$ (angles in the alternate segment are equal)
$\angle ACD=\angle ACB+\angle BCD$
$={90}^{\circ }+{30}^{\circ }$ $={120}^{\circ }$