How to find point $G$ in this configuration?

Question

Circle $A$ and circle $B$ intersect at $C$ and $D$. Given that $A = (x_1, 0)$, $B = (x_2, 0)$, and the radii of circle $A$ and circle $B$ are $r_1$ and $r_2$, respectively, then how to find $CG$?

Explain what is $r_1, r_2, c_1, c_2$ – King Tut Feb 27 '18 at 14:40 — King Tut, Feb 27 '18 at 14:40
@KingTut I'm guessing radius and center for the two circles – cansomeonehelpmeout Feb 27 '18 at 14:42 — cansomeonehelpmeout, Feb 27 '18 at 14:42
I'm guessing that too, but not sure so I asked. – King Tut Feb 27 '18 at 14:43 — King Tut, Feb 27 '18 at 14:43

score 0 · Accepted Answer · answered Feb 27 '18 at 14:39

0

Hint

You know: $ r_1\;,\; r_2 \;,\; AB=d $

let: $AG=x$

Than

$ r_1^2-x^2=CG=r_2^2-(d-x)^2 $

solve this equation for $x$.

answered Feb 27 '18 at 14:39

Emilio Novati

62,675

score 0 · Answer 2 · answered Feb 27 '18 at 14:42

0

Hint:

Look for right triangles containing $\overline{CG}$
Use Pythagoras

answered Feb 27 '18 at 14:42

cansomeonehelpmeout

12,782
3
22
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How to find point $G$ in this configuration?

2 Answers2