What is the relation between AM amp- MB in the given figure- 2AM - MB-AM - MB-AM - 2MB-3AM - 2MB-

The correct option is B AM = MB In the given figure, considering nbsp;Δs OAM and ΔOBM, we have OA = OB (Radii of the same circle) OM = OM (Common Side) ∠ OMA ...

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Standard IX

Mathematics

Perpendicular from Center to a Chord

What is the r...

Question

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

AM = MB

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AM = 2MB

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2AM = MB

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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)

$∠ O M A = ∠ O M B = 90^{\circ}$ (OM $⊥$ AB)

$\Rightarrow$ $Δ$ OAM $≅$ $Δ$ OBM by RHS criterion of congruency.

$⟹ A M = M B$ ( 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 $O M ⊥ A B,$ we have $A M = B M .$

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