Math, asked by aaaa17, 1 year ago

prove that the line joining the mid point of two parallel chords of a circle passes through the centre.

Answers

Answered by wchow
92
Recall one important thing when you are solving this question:
The perpendicular bisector of any chord passes through the center 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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Answered by sushmasharma61178
4

Step-by-step explanation:

I hope this diagram will help you

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