1. ## [SOLVED] Triangulation

S1 is located at (100,200). It's distance to the epicenter is 100 √ 10 miles
S2 is located at (400,500). It's distance to the epicenter is 200 miles
S3 is located at (700,100). It's distance to the epicenter is 100 √ 13 miles

1)What is the radius of S1? S2? S3?

2)State the equations, in standard form, for circles S1, S2, S3.

3)State the distance from the base (0,0) to the epicenter?

• $r_{S1}=100\sqrt{10} mi$
• $r_{S2}=200 mi$
• $r_{S3}=100\sqrt{13} mi$

2. Equation of circles:
• S1: $(x+100)^2+(y+200)^2=r_{S1}^2$
• S2: $(x+400)^2+(y+500)^2=r_{S2}^2$
• S3: $(x+700)^2+(y+100)^2=r_{S3}^2$

3. Finding epic center by setting the equations equal:
• $y_{S1}=\pm\sqrt{r_{S1}^2-(x+100)^2}-200$
• $y_{S2}=\pm\sqrt{r_{S2}^2-(x+400)^2}-500$
• Set $y_{S1}=y_{S2}$, you should find these 2 circles intersects at 2 points.
• There are two way to pick which point is the epic center:
1. Plug the points into to the third circle and see which one work.
2. Set $y_{S3}=y_{S1}$, or set $y_{S3}=y_{S2}$. Once again you will get 2 points. Only one will be the same as one of the points found previously. That is the point you want.