In a circle of radius 11 cm, CD is a diameter and AB is a chord of len

CE=7, DE=22-7=15
AE=x, BE=20.5-x
CE*DE=AE*BE, 7*15=x(20.5-x)
\(x^2-20.5x+105=0…2x^2-41x+210=0\)
\(2x^2-20x-21x+210=0…2x(x-10)-21(x-10)=0\)
\((2x-21)(x-10)=0…x=(10.5,10)\)
AE=20.5-10.5=10, BE=20.5-10=10.5
|AE-BE|=0.5

Ans (A)

hi dilesh can you explain how you get to:
--> (AE−BE)2=(AE+BE)2−4∗AE∗BE(AE−BE)2=(AE+BE)2−4∗AE∗BE
--> (AE−BE)2=(20.5)2−4∗105=420.25−420=0.25(AE−BE)2=(20.5)2−4∗105=420.25−420=0.25
--> AE−BE=0.25−−−−√=0.5
here?
i dont get where the equation is coming from

Think of AE as x and BE as y, where \(x + y = 20.5\); what we're looking for is \(|x-y|\). Now remember the properties that:

\((x - y)^2 = x^2 - 2xy + y^2\)
\((x + y)^2 = x^2 + 2xy + y^2\)

To get \((x - y)^2\) from \((x + y)^2\), we have to subtract \(4xy\) to get:

\((x + y)^2 - 4xy = x^2 + 2xy + y^2 - 4xy = x^2 - 2xy + y^2 = (x - y)^2\).

Therefore, we can solve as follows:

\((x - y)^2 = (x + y)^2 - 4xy\)
-> \((x - y)^2 = (20.5)^2 - 4(105)\) (because \(AE * BE = CE * DE = 7 * 15 = 105\) by the Intersecting Chords Theorem)
-> \((x - y)^2 = 0.25\)
-> \((x - y) = \sqrt{0.25} = 0.5\) or \(-0.5\)
-> \(|x - y| = 0.5\)

Answer choice A. A great solution by Bunuel, hope this explanation helps you, it took me a while to also understand this question!