SOLUTION: If a line through the center of a circle is perpendicular to a chord, then the line also bisects the chord. I have some work done with a drawing on sketchpad, but I am not sure

Algebra ->  Geometry-proofs -> SOLUTION: If a line through the center of a circle is perpendicular to a chord, then the line also bisects the chord. I have some work done with a drawing on sketchpad, but I am not sure       Log On


   

Question 60904: If a line through the center of a circle is perpendicular to a chord, then the line also bisects the chord.
I have some work done with a drawing on sketchpad, but I am not sure where to even start with writing my proof. They make no sense to me since I have not had a good teacher to teach me proofs. Thank you
Answer by asha(30) About Me  (Show Source):
You can put this solution on YOUR website!
let AB be a chord in the circle
let line XY intersect the chord at P.
let O be the centre of the circle.
OP is perpendicular to AB.
Join OA and OB.
you have 2 right angled triangles OAP and OBP.
Considering the two triangles, we have
OA = OB radii of the circle and the hypotenuse of the right triangles.
OP is common to the two triangles.
angle OPA = angle OPB =90 degrees.
therefore the two triangles are congruent.(right angle, hypotenuse and side)
hence AP =PB (corresponding parts of congruent triangles are equal)
the line OP bisects chord AB.