Given an angle at a point A and given another segment BC, construct a point D so that the angle DBC equals the given angle at A.

I'm not sure if I understand this question right.

Q. Given an angle at a point A and given another segment BC, construct a point D so that the angle DBC equals the given angle at A.

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Should I assume one of the sides of the angle a is bc and the end point of the other side is the point d ?

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Not quite. One of the sides of the reproduced angle is $bc$, and the endpoint of the other side is $d$. – David Mitra Jan 30 '13 at 17:28
@DavidMitra - I might be misinterpreting what you said, but how is that different from what I intended on assuming ? – devcoder Jan 30 '13 at 17:52
I may be misinterpreting you. It seemed you wanted to take angle $a$ and just call one of its sides $bc$. You have to, of course, reproduce the angle on the line segment $bc$ as given. (The reproduced angle has to be called something other than "$a$"). – David Mitra Jan 30 '13 at 17:56
@DavidMitra - You are right. But I am still confused on how to reproduce the angle a on the line segment bc? – devcoder Jan 30 '13 at 18:03
Hint: 1) Draw an arc, with arbitrary radius, on angle $a$ with center the vertex of $a$. Call the points of intersection of $a$ and the arc $e$ and $d$ . 2) Draw an arc of radius $d$ with center $b$ on the segment $bc$ 3) How could you find the points on the arc drawn in 2) that correspond to the points $d$ and $e$? – David Mitra Jan 30 '13 at 18:07