. What's the length of the radius of the circle?

Question

Two chords AB and CD perpendicularly bisect each other at the point E.The length of two chords are 2a and 2b.The distance from the intersecting point to the center of the circle is c.

Answer 1

If you can use the theorem that the perpendicular bisector of the chord of a circle must pass through the center, then it follows that, if two chords are perpendicular bisectors of each other, they must both path through the center of the circle.

 

Any chord that passes through the center of the circle is, by definition, a diameter.  

 

The only place two distinct diameters of a circle can intersect is the center of the circle.

 

Therefore, point E is the center of the circle, c =0, 2a = 2b, and a=b=length of the radius, which is half the length of the diameter.