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 find the value of $\angle CDB$ [3 Marks]

Answer 1

$\angle ACB={90}^{\circ }$ [Angle in the semicircle]
$\angle BCD={30}^{\circ }$ [Angles in the alternate segment are equal] [1 Mark]

$\angle ACD=\angle ACB+\angle BCD$
$\angle ACD={90}^{\circ }+{30}^{\circ }$
$\angle ACD={120}^{\circ }$ [1 Mark]

$\angle CDB={180}^{\circ }-({30}^{\circ }+{120}^{\circ })$ [Sum of angles in a triangle]

$\angle CDB={180}^{\circ }-{150}^{\circ }$
$\angle CDB={30}^{\circ }$ [1 Mark]