2+ [ Inscribed angle, based on the diameter ]

$A B$ is the diameter of the circle, $B C$ is the tangent. The secant $A C$ is divided by the circle at point $D$ in half. Find the angle $D A B$.

#
An inscribed angle that subtends a diameter is $90^{\circ}$.

## Solution

In triangle $A B C$, the height $B D$ is also a median. Therefore, this triangle is isosceles. Hence, $\angle D A B=45^{\circ}$.

## Answer

$45^{\circ}$