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20 14 a problem of mathematics in Laiwu senior high school entrance examination
Connect OC, extend the intersection O to G, and connect eg.

Then < g+<; GCE=90

Because e is the midpoint of arc AB,

Therefore, < ABE =< Economic cooperation always belongs to.

DC=DF

So < ECD = < computational fluid dynamics (CFD)

< CFD = < CEB+<; ABE = & ltG

So < DCE = <; G

So < OCD =<d ce+<; GCE = & ltg+& lt; General education certificate

So OC is perpendicular to CD

So DC is the tangent of circle O.

Connecting BC

From 1, the triangle BEF is similar to the triangle EBC.

So BE/EC=EF/BE.

So ef * EC = be 2 = 4/9r 2.

Because f is the quartering point of AB.

So FB/AF= 1/3.

On EF/AF=FB/FC from chord intersection theorem

So EC=4EF.

So EC=r/3