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prove that OM bisect AB .IF OM PERPENDICULAR AB

Posted by Harsh Agrawal 8 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Shweta Gulati 8 years, 5 months ago

The perpendicular from the centre to the chord bisects the chord

In the diagram below, AB is the chord of a circle with centre O.

OM is the perpendicular from the centre to the chord.

Look at triangles OAM and OBM.

The hypotenuses (OA and OB) are the same, as they are both the radius of the circle.

OM is common to both triangles.

OMA and OMB are both right angles.

Triangles OAM and OBM are congruent (RHS), so it follows that AM = MB.

Therefore, M is the midpoint of AB, and the chord has been bisected.

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This content has been hidden. One or more users have flagged this content as inappropriate. Once content is flagged, it is hidden from users and is reviewed by myCBSEguide team against our Community Guidelines. If content is found in violation, the user posting this content will be banned for 30 days from using Homework help section. Suspended users will receive error while adding question or answer. Question comments have also been disabled. Read community guidelines at https://mycbseguide.com/community-guidelines.html

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