A1H1 = A2H2 pending

In a circle where a chord BC subtends angles at A1,A2 on the circumference.
Let H1,H2 be orthocenters of A1BC and A2BC.
Then A1H1 = A2H2
Why?
Since A1H1 = 2R.cosA1
A2H2 = 2R.cosA2
Circumradius is same and angles are also same.

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