# Circle geometry proof

1. Aug 8, 2017

### Mr Davis 97

1. The problem statement, all variables and given/known data
Prove that any chord perpendicular to the diameter of a circle is bisected by the diameter.

2. Relevant equations

3. The attempt at a solution
I was thinking that maybe I could form two triangles, show that these triangles are congruent, and then conclude that the two lengths of the chord cut by the diameter are equal in length. But I can't seem to prove congruence.

2. Aug 8, 2017

### SammyS

Staff Emeritus
What triangles are you forming ?

3. Aug 8, 2017

### Mr Davis 97

Oh wait... Let X be the intersection of the chord and the diameter. If I form triangles with the radius, then I get that the hypotenuses are equal, but I also get that the segment from X to the center of the circle is the same for both triangles, so they are congruent by SSS (since the other side for both triangles comes from the Pythagorean theorem).

4. Aug 8, 2017

### SammyS

Staff Emeritus
Yes, the triangles are congruent, but not by SSS. That would require that you assume the thing you are to prove.