Hello! I'm glad to help you solve it. To remind you, your topic is wrong, not AC=BA, but AC=BC.

Proof: It can be seen from the problem that: ∠CAF+∠ACF=90 degrees; < BCF+< ACF = 90 degrees;

So: ∠CAF=∠BCF

And because: ∠F=∠BDC=90 degrees, and AC=BC.

So: the triangular AFC and the triangular CDB are congruent.

So: AF= CD CF=BD.

Because: CF=CD+DF

So: CF=AF+DF

So: BD=AF+DF.

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