This is hard

[Sillysidley]

1. What is the arithmetic mean, expressed as a common fraction, of the solutions to|10x|-sqrt(10x)=0

2. Triangle ABC is such that AB=8, AC=9, and BC=10 cm. The bisector of the interior angle BAC intersects BC in a point M. What is the length of the segment BM? Give you r answer as a common fraction in lowest term.

These are tricky. I have worked on them for hours, and don't know what they are.

If anyone wants interesting problems tell me. ( I kow the answers to those )