Question

M and n are the mid point of two equal chords Ab and CD respectively of a circle with center o prove that angle Bmn = angle dnm

Answer 1

..............................

Answer 2

∠BMN =   ∠DNM

Step-by-step explanation:

AB = CD

=> AM = BM = CN = DN

OM ⊥ AB  & ON⊥CD

∠BMO = ∠AMO = 90°  & ∠CNO = ∠DNO = 90°

OM = ON

in ΔOMN

OM = ON

=> ∠OMN = ∠ONM

∠BMN = ∠BMO - ∠OMN

=> ∠BMN = 90° - ∠OMN

∠DNM = ∠DNO - ∠ONM

=> ∠DNM = 90° - ∠ONM

∠OMN = ∠ONM

=> 90° - ∠OMN = 90° - ∠ONM

=> ∠BMN =   ∠DNM

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