Question

In a circle with center 'O'.AB is a chord and 'M' is its midpoint.Now prove that OM is perpendicular to AB

Answer 1

Step-by-step explanation:

M is the midpoint of AB

So, AM = MB

Now draw Radius OA And OB

Then, In ∆OAM and ∆OBM

OA = OB (Radii of the same circle)

AM = MB ( M is the midpoint)

OM = OM (Common Side)

So, ∆OAM= ∆OBM (By SSS Test)

angle OMA= angle OMB. (C.A.C.T)............1

But, angle OMA + angle OMB = 180° (linear pair)

So, 2(angle OMA) = 180° (from 1)

Angle OMA = 180÷2

Angle OMA = 90°

Thus, OM is perpendicular to AB.