two chords intersect at a point on a circle and diameter through this point bisect the angle between the chords. Probe that chords have the same length ?
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Step-by-step explanation:
In △OEB&△OEC, they are congruent (SAS)
Three lines are concurrent at E.
Three vertically opposite angles are same. Let them be p, q, r.
BE=EC→(1)
△AEO&DEO are congruent too (SAS)
DE=AE→(2)
Total lengths of chord
AE+EC=DE+EB (Same) (From (1) &(2))
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