Found Out I May Have SECRET Half-Siblings. What Do I Do?

Yesterday I found in my filtered message requests on Facebook Messenger a woman asking me if *Jerry is my father. After I said yes, she proceeded to tell me "he has other kids" and she was one of them. 😨
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We got to talking and she told me about herself. She's 41 so that means my father had to of been in his 20s when she was born. She gave me the names of my father's TWO other supposed kids. At first I didn't believe her. 
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But then she told me some incriminating facts:
1. According to ancestry.com, Jerry is their father. 
2. Also on ancestry, they found out they were related to a guy named *Eli. And I have an Uncle Eli on my father's side. 
3. He was around them for a little while. She insinuated it was mostly unrelated to the children. She said it was a different time then, the whole "drugs sex and rock and roll" era. 
4. She said she called my father years ago, after me and my sister were born, and he apologized, said he'd changed a lot since then, and his wife "understood because she was a Sunday School teacher." My mother was in fact a Sunday School teacher. But he didn't want his kids (me and my sister) to find out. 
5. She found ME through my mom's profile. She had to know who my mother was to do so. Especially since she now lives in another state. 
6. The other two live minutes from my hometown, a town my father has never left. 
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Little background: I'm 21. My sister is 24. We've had a relatively normal childhood. My parents have been together forever and are still married. It was a great childhood actually. My dad quit drinking as soon as my mom was pregnant with my older sister. He quit smoking before I got married - about 3 years ago. He's been a doting father, a father really invested in our lives. A loving father too. 
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This woman gave me the name of their mother. I don't know what to do with this information. I don't want to approach this with my parents in the wrong way where it sounds like I'm judging them or hurt them in any way. But I also want to get the facts. I'm like 60/40 on believing this woman. It's just the stuff she knew was sort of true. 
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Should I just bring it up with my dad?
Should I ask one of my dads oldest friends if he knows the mother? Ever slept with her?
Should I ignore this?
*Names changed for protection