Question

in the given figure equal chords AB and CD of a circle with center O intersect at right angles at E=, if M and N are mid points of AB and CD respectively, prove that angle EOM =45°

Answer 1

hi friend...
:)
here is the answer:

AB and CD are equal chords of the circle with centre O. M is the mid point of AB and N is the mid point of CD.
∠MEN=90°   (Given)
OM⊥AB     (The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord)
∠OME=90°
ON⊥CD     (The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord)
∠ONE=90°
∴OMEN is a rectangle.⇒∠EOM=90°       (Diagonal of a rectangle bisects the opposite angles)

hope this helps u....
:-)