Question

in the figure, equal chord AB and CD of a circle with centre o intersect at right angles at E.if M and N are the mid points of AB and CD respectively , prove that angle EOM=45 DEGREE

Answer 1

we know that mid point of chord joining the center is perpendicular to chord ∴∠ ONE = ∠ OME = 90 °
Also ∠MEN = 90 °
∴ ONEM is a square of rectangle. Again equal chord are equidistance from the center  ∴ OM = ON  ⇒ONEM is a square.  we know that diagonal of a square bisect the angle so 
∠ OEN=∠ OEM=90/2=45°
hence proved