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Assuming that there's a circle subscribing the traingle ABC with center D and radious DA = DC= DB.

AC must be a diagonal hence, Angle ABC is a 90• and Traingle ABC is a right angled traingle. Now it's given that angle BAD is 50, so we can calculate Angle BCA (180-90-50 = 40•)

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The diagram shows that BD bisects AC into 2 and is actually equal to AD and DC.

This immediately shows that ABC is a right-angled triangle where BD = median to hypotenuse (AC) where median is essentially half the length of hypotenuse (AC). Therefore angle BCA is essentially 40 degrees (without using calculation of the angles of the smaller triangles).
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