Question

how would you prove that a straight line drawn from the centre of a circle to bisect a chord, which is not a diameter,is at right angles to the chord ?

Answer 1

let the centre be O and the chord be AB and the line from the centre be OL
now join O to A and B =>
in triangles AOL and BOL
OA = OB (radii)
AL=BL (bisects the chord)
OL=OL ( common)
therefore triangles AOL and BOL are congruent =>angle ALO = angleBLO
and since ALB is the straight line of chord
=> angle ALO= angle BLO= 90degrees