tex] CML
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TheAnimeGirl
High School
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♡[tex] \underline{ \underline{ \text{Question : }}} [/tex] In the given figure , L and M are the mid-points of two equal chords AB and CD of a circle with centre O. Prove that :
i.
[tex] \angle[/tex]OLM = [tex] \angle[/tex] OML
ii. [tex] \angle[/tex] ALM = [tex] \angle[/tex] CML
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(Based on todays review)
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msm555
Answer:
Given: chord AB=chord CD
L and M are the mid-points of two equal chords AB and CD of a circle
we have
(Equal chords are equidistant from the centre)
In ∆ OLM
OL = OM
<OLM= <OMLbase angles
opposite to equal sides of a A
<OLA = <OMC(Each = 90°being perpendicular) Adding
<OLM+<OLA = <OML+<OMC
<ALM=<CML
Hence proved.
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