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Question
What is the relation between AM & MB in the given figure?
What is the relation between AM & MB in the given figure?
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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∘ (OM⊥AB)
⇒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 OM⊥AB, we have AM=BM.
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∘ (OM⊥AB)
⇒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 OM⊥AB, we have AM=BM.
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