Prove that the line joining the mid-points of two parallel chords of a

1.	Prove that the line joining the mid-points of two parallel chords of acipcle passes through the centre of a circle.
Answer» ∠BOC =∠OAZ = 90° (corresponding angles, OC//YZ)∠COA =∠XBO = 90°(corresponding angles, OC//WX)∠AOB= ∠BOC + ∠COA=180° So AOB is a straight line. Therefore AB passes through O.

Prove that the line joining the mid-points of two parallel chords of acipcle passes through the centre of a circle.

Answer»

∠BOC =∠OAZ = 90° (corresponding angles, OC//YZ)∠COA =∠XBO = 90°(corresponding angles, OC//WX)∠AOB= ∠BOC + ∠COA=180°

So AOB is a straight line. Therefore AB passes through O.