Prove that the line joining the mid-point of a chord to the centre of the circle passes through the mid-point of the corresponding minor arc.

Explanation

Given : C is the mid-point of chord AB.

To prove : D is the mid-point of arc AB.

Proof: In `triangleOAC` and `triangleOBC`

`OA=OB` (radius of circle)

`OC=OC` (common)

`AC=BC` ( C is the mid-point of AB)

`triangleOAC~=triangleOBC` (By SSS)

`angleAOC=angleBOC` (By CPCT)

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