Question

a) 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.
​

Answer 1

Step-by-step explanation:

Consider AB || CD and POQ as the diameter

It is given that ∠PEB = 90o

From the figure we know that AB || CD and ∠PFD and ∠PEB 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 bisects 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.Read more on Sarthaks.com - https://www.sarthaks.com/727518/prove-diameter-circle-perpendicular-parallel-chords-circle-perpendicular-other-bisects

Answer 2

Step-by-step explanation:

Answer:-

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.

PICTURE IN ABOVE ATTACHMENT.

HOPE IT'S HELP YOU ❤️✌️❤️.