Bunuel wrote:
aakrity wrote:
we are given that AB=BC=CD
AB is the radius of the circle, so AB=AD
This makes ABCD a square. Therefore, BD and AC are the diagonals of the square. Angle A, B, C, D = 90 and hence x=45
Why is this not considered that ABCD is a square?
ABCD is not a square it's a rhombus (the diagonals are not equal).
Bunnel,
So Diagonals are 'angle bisectors' both in a Rhombus (not congruent here) and a Square. But it's not the case in a rectangle where they are congruent and perpendicular bosectors alone.
Is my understanding accurate?
I've read that every point on an angle bisector is equidistant from both the adjacent sides. Is there any other way to identify whether a diagonal is also an angle bisector?
Thank you