This document appears to be a geometry-related exercise involving trapezoid $ABCD$, with specific information about side lengths, angles, and parallelism. The task seems to involve proving certain geometric relationships based on the given conditions, such as:

• $AB \parallel DC$
• The lengths $AB = a$ and $CD = b$ with $a < b$
• $\angle C = 60^\circ$

Let me break down the steps that are presented:

1. Part a

You are asked to prove that $AD - BC = 1$, based on the given information and geometric setup.

2. Part b

It appears you need to calculate a specific length or angle, perhaps related to $BD$, as it’s mentioned in the condition that the length of $BD$ is $a = 4$ and something related to its properties.

3. Part c

Here, you're likely tasked with solving a few geometric properties, potentially using trigonometric identities or transformations based on the initial setup.

Would you like me to guide you through solving the problem step by step or focus on a specific part of the task? Let me know if you need detailed explanations or a breakdown of any specific section!