See the diagram

let O be the center of the circle

therefore, AE is the diameter

AE = AD + DE

AE = 5 + 3

AE = 8 cm

therefore,

AO = r

AO = 8 ÷ 2

AO = 4 cm

In triangle AOC

AO = OC = 4 cm (radii)

AO = OC = AC = 4 cm (given AC = 4cm)

therefore,

Triangle AOC is an equilateral traingle

In triangle AOB

AO = OB = 4 cm (radii)

therefore,

angle OAB = angle OBA (angles opp. to equal sides are equal)

Therefore

angle OBA = angle OAB = angle OAC = angle OCA (angle OAB = angle OAC given, angle OAB = angle OBA, angle OAC = angle OCA)

In traingles AOB and AOC

AO is common

angle OAB = angle OAC (given)

angle OBA = angle OCA (proved above)

therefore by AAS congruence rule

Triangle AOB = Triangle AOC

therefore by CPCT

AB = AC

AB = 4 cm

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