Question

Ac and bd are the chords of a circle bisect each other show that ac and bd are the diameters

Answer 1

Let AC and BD are the chords of a circle which bisect each other.

1. We have to prove that AC and BD are diameter

Since it is given that AC and BD are the chords of a circle which bisect each other.

Now in ΔABD,

∠A = 90

So BD is a diameter   (since angle in a semi-circle is 90)

Again in ΔBCD,

∠D = 90

So AC is a diameter   (since angle in a semi-circle is 90)

So AC and BD are the diameter.