If one of your employees has personal problems (at home) that affect his performance, will you:

A mix of A. and B. sometimes the employee would not want to discuss personal issues at work so it is up to the employee.  If he is willing to discuss then I would get involved and try to help him out.  If not then I would give him the moral support and the space to fix his issues to have a clear head at work. I would also help him to know how to concentrate at work and leave personal matters at home so that it would not negatively affect his career.

Combination of  A & B

"B" and that too if asked for.

A. Get involved to help him solve his problems

This will be the perfect way to solve the problem and improve my project, I think all my employees will appreciate that and they will feel more satisfied to give the work more and more.

I feel personally that, many problems that are persisting at home (in the current times) are not resolvable as in the case of what has been faced by old generations, except for financial issues.  Getting involved in personal affairs will invite much troubles to the employee if the involvement is not apt and adequate to arrive at an amicable settlement.

What we can do is a moral support and ease of work pressure with some lenient attitude to help him to resolve the personal issues by his own source. Depending upon the nature and character of employee any financial assistance that may help him to resolve the issue can be done, if the policies of the company are flexible in nature..or support for his raising a loan from external source depending upon his ability to repay on the basis of self generated income. 

Diffinetly it will affect him, Best thing is when you are at office leave your personal issues out of the door. When you are out of office leave your office problems inside that door which allows you to exit. Work and home both are related and important one should not be affected by the other.

The best answer is B

That depends on the relationship between us.

But formally:

C. Force him to keep his problems at home.

Depending on the problem type and details any of the given answers could be applied. but in all cases as this problem has impact employee's performance you will be involved.

B would be the best choice. Getting involved in someones personal problems may cause more harm than good as the professional factor dissolves making you to overlook and question any decisions that are supposed to be taken for that employee.  Give moral support but also make sure to let the employee know that  personal life should not affect the his/her responsibilities as at the end of the day in a team if one goes down it can take the entire team with him/her.

You only get involved if the employee kindly asks you to do so and ask for your help in resolving those issues relating to their personal life at home. Personally in my opinion a professional person would not bring their personal issues to work they know how to control their emotions visibly. However as humans the majority of us are affected and often misguided by our emotions. I agree with Doha Shawki, give them the support they need and help them. I would have constant one-to-ones with the individual and ensure they are okay, give them advice if needed and only of I am sure of it, show them you are supportive and empathise with their situation. Sometimes all we need is someone to listen, so we can unload the burden tightening in our chest. Also being a manager is a profession which in time will probably be given to someone else, being human is everlasting so be a human being who understands the problem and step down from your profession with limits and boundaries.