Q6 of 100 Page 16

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.

Given that,

C is the mid-point of chord AB


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


Proof: In


OA = OB (Radius of circle)


AC = OC (Common)


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


Then,


(By SSS congruence rule)


∠AOC = ∠BOC (By c.p.c.t)


m (A) = m (B)


A B


Here, D is the mid-point of arc AB


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