Question

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

• A. AM = MB
• B. AM = 2MB
• C. 2AM = MB
• D. 3AM = 2MB

Answer 1

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)

$\angle OMA=\angle OMB={90}^{\circ }$ (OM$\perp$AB)

$\Rightarrow$$\Delta$OAM $\cong$ $\Delta$OBM 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 $OM\perp AB,$ we have $AM=BM.$