It looks like you're asking for the lengths of segments $BD$ and $BC$, but I need more information to proceed. Here are a few things that could help:

1. Are there any diagrams or figures available?
2. Is this question related to geometry (like a triangle or polygon)?
3. Are there any given angles or side lengths for the shape?
4. Does this involve coordinate geometry or trigonometry?

Feel free to upload an image or provide additional data, and I’ll walk you through the solution.

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Here are five questions to help us dig deeper:

1. Is this problem related to a triangle? If so, what are the known sides and angles?
2. Are $BD$ and $BC$ in a right-angled triangle?
3. Is the shape inscribed in a circle, or does it involve a specific theorem (like the Pythagorean theorem)?
4. Are coordinates provided for points $B$, $D$, and $C$?
5. Is this problem part of a larger proof or construction task?

Tip: When working with geometry, try sketching or visualizing the problem, as it often provides insight into hidden relationships.