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Prove that the line joining the mid-points of the two parallel chords of a circle passes through thecentre of the circle.10. |
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Answer» The perpendicular bisector of any chordpasses through thecenter of the circle. So when you construct the diagram, remember to mark the right angles (∠OAZ and∠OBX in the diagram). Also, you need to identify what you are supposed to prove (joining mid point passes through the center). So you need to prove that AOB is a straight line.To do that, we can construct another line OC//WX//YZ. The proof ∠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. |
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