THEOREM 3The perpendicular from the centre of a circle to a chord bise

1.	THEOREM 3The perpendicular from the centre of a circle to a chord bisects the chord. INCERT
Answer» Angles OMA and OMB are both right-angles. OA is thehypotenuseof triangle OAM. OB is the hypotenuse of triangle OBM. OA = OB as both areradiiof the circle. OM is common to both triangles. Therefore, triangles OAM and OMB arecongruent(RHS – right-angle, hypotenuse, side). Therefore, the remaining sides of the triangles are equal, AM = MB. So, M must be the mid-point of AB, and the chord has been bisected.

THEOREM 3The perpendicular from the centre of a circle to a chord bisects the chord. INCERT

Answer»

Angles OMA and OMB are both right-angles.

OA is thehypotenuseof triangle OAM.

OB is the hypotenuse of triangle OBM.

OA = OB as both areradiiof the circle.

OM is common to both triangles.

Therefore, triangles OAM and OMB arecongruent(RHS – right-angle, hypotenuse, side).

Therefore, the remaining sides of the triangles are equal, AM = MB.

So, M must be the mid-point of AB, and the chord has been bisected.