In the given figure, the circle with centre o has chord ab = bc = cd= de. Prove that ad = be
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Given : the circle with centre o has chord ab = bc = cd= de.
To Find : Prove that AD = BE
Solution:
Join AD and BE
AD & BE intersects at AP
∠BAD = ∠BED By same arc BD
=> ∠BAP = ∠DEP
∠EBA = ∠EDA by same arc AE
=> ∠PBA = ∠PDE
AB = DE given
=> Δ APB ≅ Δ EDP ( ASA criteria)
PB = DP
AP = EP
PB + EP = DP + AP
=> BE = AD
QED
Hence Proved
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