In a circle of radius 11 cm, CD is a diameter and AB is a chord of length 20.5 cm. If AB and CD intersect at a point E inside the circle and CE has length 7 cm, then the difference of the lengths of BE and AE, in cm, is
Solution
In figure AE*BE=CE*DE (The intersecting chords theorem)
=> 7*15= x(20.5-x) (Assuming AE=x)
=> 210=x(41-2x)
=> $$2x^2$$-41x+210=0
=> x=10 or x=10.5 => AE=10 or AE=10.5 Hence BE = 20.5-10=10.5 or BE = 20.5-10.5=10
there is theorem saying line drawn from centre to chord bisects it,so y did not AB got divided into 2 equal parts of 10.25 cm eac cuz OE is a line going from centre to chord so it should divide AB in to 2 equal parts,please tell where am I wrong
The theorem says "the perpendicular from the centre to the chord bisects the chord". Hence for CD to bisect AB , it needs to be perpendicular to AB, which is not the case in this question. Hence CD doesn't bisect AB. Hope it helps. Thanks
