Math, asked by bagegloria, 1 year ago

Prove that the line joining the mid-point of two parallel chord of a circle passes through the centre

Answers

Answered by ALIFIYA007
3
yes its easy first of all u need to draw a circle with two equal chord and tldraw perpendicular besector of each
thus proobed
Answered by Anonymous
16

Answer:

Let AB and CD be two parallel chords having P and Q as their mid-point respectively. Let O be the centres of the circle. Join OP and OQ and OX || AB or, CD.

Now, P is the mid-point of AB.

OP \perp AB

=> \angleBPO = 90°

but,

OX || AB

•°• \angle POX = \angle BPO

=> \angle POX = 90°

Similarly, Q is the mid-point of CD

= OQ \perp CD

= \angle CQO = 90°

But,

OX || CD

•°• \angle XOQ = \angle CQO = 90°

= \angle POX + \angle XOQ= 90° + 90° = 180°

= POQ is a straight line.

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