The problem presented in the image involves a geometric figure, specifically a triangle $\triangle ABC$ inscribed in a circle with center $O$, focusing on relationships and constructions involving tangents, perpendiculars, and angles. Here is a step-by-step breakdown of the problem and the requirements based on my interpretation:

1. Given: Triangle $ABC$ inscribed in a circle with center $O$.

   • The point $A$ is on the circumference, as are points $B$ and $C$.
   • $AB$ is a tangent line at point $A$, which implies that $AB \perp OA$, as tangents to circles are perpendicular to the radius at the point of tangency.

2. Tasks:

   • (a) Draw the perpendicular from point $B$ to line $OC$ and label this intersection as $H$.
   • (b) Draw line $AK$, where $AK$ is perpendicular to $OB$, and label the intersection point.
   • (c) Prove that the angles are congruent, specifically $\angle OCB = \angle OAB$.

The goal of this problem seems to be establishing perpendicularity and angle congruence based on the properties of the inscribed circle and tangent lines.

Would you like detailed solutions to each part of this problem? Here are five related questions for deeper exploration:

1. How do we prove that a tangent to a circle is perpendicular to the radius at the point of tangency?
2. What properties of inscribed angles can we use to relate angles $OCB$ and $OAB$?
3. How can we construct perpendicular lines geometrically in circle-related problems?
4. What other geometric properties can be derived from points lying on a circle with given tangent lines?
5. How does the inscribed angle theorem apply to triangles within a circle?

Tip: When working with circle problems, always consider the relationships between radii, tangents, and inscribed angles—they often provide the key insights for proving perpendicularity and angle congruence.