# Geometry proof

• Oct 4th 2008, 06:49 AM
DJ Hobo
Geometry proof
A radius drawn to bisect a chord in a circle will always meet the chord at 90 degrees.

Use a mathematical method (that does not use vectors), to prove this.

I've never been too great with geometric proofs (Headbang)
• Oct 4th 2008, 07:14 AM
skeeter
let the chord be segment AB. let the circle center be point O.

let M be the intersection point of the bisecting radius and chord AB.

M is the midpoint of AB ... why?

now, prove that triangle OMA is congruent to triangle OMB, then use corresponding parts of congruent triangles to show that angle OMA is congruent to angle OMB.

from this point, it should be easy to show that OM is perpendicular to AB.
• Oct 4th 2008, 07:22 AM
DJ Hobo
Quote:

Originally Posted by skeeter
M is the midpoint of AB ... why?

I don't understand that sentence. That statement is information that was given in the question, isn't it?

As for everything else you said, I understand and was very helpful. Thanks :D
• Oct 4th 2008, 07:37 AM
skeeter
formally, you can't just say M is the midpoint of AB ... the reason must be given, i.e. "definition of a segment bisector".
• Oct 4th 2008, 07:39 AM
DJ Hobo
Quote:

Originally Posted by skeeter
formally, you can't just say M is the midpoint of AB ... the reason must be given, i.e. "definition of a segment bisector".

Errr... sorry, I don't think I fully understand what you said.
• Oct 4th 2008, 08:10 AM
skeeter
you do understand that every statement in a proof requires a reason, correct?

that's all I'm trying to tell you.
• Oct 4th 2008, 08:12 AM
DJ Hobo
Quote:

Originally Posted by skeeter
you do understand that every statement in a proof requires a reason, correct?

that's all I'm trying to tell you.

Uhmm.. I think so.. I'm not too used to proofs yet (Worried)