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.

Question

Philoid · Accepted Answer

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