Question

I WILL MARKYOU BRAINLIEDT FOR A QUICK AND GOOD ANSWER Proof that the perpendicular bisector of a chord passes through the centre of the circle ⭕️

Answer 1

Let  be the center of the circle. Draw , a chord  and let  be its midpoint.



Construct  perpendicular to latex R as shown above. We show that  is on .

Theorem

The perpendicular bisector of a chord passes through the center of a circle.

Proof

Join ,   and .

Since  is  the center of the given circle,  because both of them are radii of the same circle.

Also,  since  is the midpoint of . In addition,  because a segment is congruent to itself.

So, by the SSS Congruence Theorem, .

Also,  and both of them are right angles. Therefore,  is a part of the two right triangles which means that it is on . This is what we want to prove.