Question

In a circle with centre O. AB is a chord and M is its midpoint now prove that OM is perpendicular to AB

Answer 1

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Explanation:

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Answer 2

Given ,

Center of the circle is O.

Chord of the circle is AB.

AB is a chord and M is its midpoint.

To find ,

OM is perpendicular to AB.

Solution ,

In Δ OAM and Δ BOM

As AB is the chord and M is the midpoint :

AM = MB

∠OAM = ∠OBM

As the Δ OAM and Δ BOM has the same side :

OM = OM

By side angle side property we can say that :

Δ AOM = Δ BOM

In Δ OMA and Δ OMB

OA = OB

As radius of the circle is the same

The center of the circle is the only point within the circle that has points on the circumference equal distance from it.

Hence, OM is perpendicular to AB is proved.