The internal bisector of ∆ABC at ∠A cuts BC on D and cuts the circumcircle at E. If DE = 6cm, AC = 8cm and AD = 10 cm, then find the length of AB?
Join EC, From the diagram, AE = AD + DE AE = 10 + 6 = 16 cm ∠ABC = ∠CEA (Similar Chord Theorem, In, ∆ADB and ∆AEC, (AB )/(AE )=(AD )/(AC )        (Similar triangle) (AB )/(16  )=(10  )/(8  )    AB = 20 cmÂ
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