<|im_start|>user
I am supposed to do homework right now but I'm not motivated enough to get started. Could you give me a good reason to start?<|im_end|>
<|im_start|>assistant
Absolutely, here are a few reasons why you should start your homework:

1. **Knowledge and Skills**: Homework helps you practice what you've learned in class, reinforcing your understanding of the material. It's an opportunity to delve deeper into the subject and gain more knowledge and skills.

2. **Responsibility and Time Management**: Doing homework teaches you responsibility, discipline, and how to prioritize tasks. These are valuable life skills that will be beneficial in the future, both in your personal life and career.

3. **Better Grades**: Homework often contributes to your final grade. By doing your homework and doing it well, you increase your chances of getting a better grade in the class.

4. **Preparation for the Future**: Homework can help prepare you for the next class or for exams. It's a way to review and make sure you're ready for future challenges.

5. **Avoid Stress**: Leaving homework until the last minute can cause unnecessary stress and anxiety. By starting now, you can work at a comfortable pace and avoid a last-minute rush.

Remember, it's okay to take breaks while doing your homework. Studies show that taking short breaks can actually improve focus and productivity. So start your homework now, take it one step at a time, and remember to give yourself a break when you need it. You've got this!<|im_end|>
<|im_start|>user
I need help with my math homework. Here's the problem:

> "Let ABC be an acute triangle with orthocenter H. The circle passing through H with center the midpoint of BC intersects the line AH at two points, one of which is interior to ABC. Let D be the foot of the altitude from A to BC. Prove that AD is tangent to the circle passing through H with center the midpoint of BC."<|im_end|>
<|im_start|>assistant
To prove that AD is tangent to the circle passing through H with center the midpoint of BC, we will use the fact that if a line is tangent to a circle, then it is perpendicular to the radius at the point of tangency.

Let O be the midpoint of BC, and let E be the intersection of AH and the circle with center O. Since O is the midpoint of BC, DE = DH (because they are both radii of the same circle). Also, since H is the orthocenter, ∠BHA = 90° - ∠C.

Now consider triangle AHD. We have:

∠AHD = 180° - ∠AHB - ∠DHA
= 180° - (90° - ∠C) - ∠C
= 90°

Since ∠AHD = 90°, AD ⊥ HD. But HD is a radius of our circle at point D. Therefore, AD is tangent to the circle passing through H with center O (the midpoint of BC).<|im_end|>
