Question

10. Prove that the diameter of a circle perpendicular to one of the two
parallel chords of a circle is perpendicular to the other and bisects it.

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Answer 1

a) when they are in contact only

Answer 2

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Prove that the diameter of a circle perpendicular to one of the two parallel chords of a circle is perpendicular to the other and bisects it.

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Consider AB∥CD and POQ as the diameter.

It is given that ∠PEB = 90°

From the figure, we know that AB∥CD and ∠PED are corresponding angles.

So we get,

∠PFD =∠PEB

It can be written as —

PF∠CD

In the same way —

OF⊥CD

Perpendicular from the centre of a circle to a chord bisect the chord.

So we get —

CF = FD

Therefore it is proved that the diameter of a circle perpendicular to one of the two parallel chords of a circle is perpendicular to the other and bisects it.

Explanation:

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