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Question

What is the relation between AM & MB in the given figure?


A

AM = MB

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B

AM = 2MB

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C

2AM = MB

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D

3AM = 2MB

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Solution

The correct option is A

AM = MB


In the given figure, considering Δs OAM and ΔOBM, we have

OA = OB (Radii of the same circle)

OM = OM (Common Side)

OMA=OMB=90 (OMAB)

ΔOAM ΔOBM by RHS criterion of congruency.

AM=MB ( By C.P.C.T)

Alternate:
We know that the perpendicular drawn from the centre of a circle to the chord bisects the chord.
Since OMAB, we have AM=BM.


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