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L and M are mid points of two equal chor...

L and M are mid points of two equal chords AB and CD of a circle with center O. Prove that `/_OLM=/_OML` and `/_ALM=/_CML`

Text Solution

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`PQ=SR`
`(PQ)/2 = (SR)/2`
`XQ = YR`
now `/_ `OCM is an isoceles `/_ ~ /_ O`
now`/_ ALM = /_ALO - /_OLM`
`= 90 - /_OLM`
`/_CML = /_CMO- /_OML = 90 - /_OML`
by comparing the 2 equations
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