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Question
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.
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Solution
Given: C is the midpoint of chord AB
To prove: D is the midpoint of arc AB Proof:∠
In Δ OAC and ΔOBC
OA=OB [Radius of circle]
OC=OC [Common]
AC=BC [C is the midpoint of AB]
Then, ΔOAC = ΔOBC [By SSS condition]
`∴∠AOC=∠BOC` [ c. p.c.t ]
`⇒m(AD)=M(BD)`
`⇒AD≅ BD `
Here ,D is the midpoint of arc AB
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