Question 559949
a rhombus ABCD of side 4 cm and diagonal 5 cm is constructed.measure angle ABC.find the point R on AD such that RB=RC.
<pre>
{{{drawing(300,400,-3,3,-4,4,
line(-2.5,0,2.5,0), line(-2.5,0,0,sqrt(9.75)),line(2.5,0,0,sqrt(9.75)),
line(2.5,0,0,-sqrt(9.75)),line(-2.5,0,0,-sqrt(9.75)),
locate(-.1,3.4,A), locate(2.6,.1,D), locate(-.1,-3.1,C), locate(-2.7,.1,B)
 )}}}

Get a protractor and measure angle ABC.  I get 103°.

To find R:

Take a compass and straight edge and construct the perpendicular
bisector of BC. That's the green line.  Then R will be the point 
where the green perpendicular bisector of BC intersects AD. 
Then RB=RC. (Triangle RBC is isosceles) 

{{{drawing(300,400,-3,3,-4,4,
line(-2.5,0,2.5,0), line(-2.5,0,0,sqrt(9.75)),line(2.5,0,0,sqrt(9.75)),
line(2.5,0,0,-sqrt(9.75)),line(-2.5,0,0,-sqrt(9.75)),
locate(-.1,3.4,A), locate(2.6,.1,D), locate(-.1,-3.1,C), locate(-2.7,.1,B),
green(line(-9,-7.766215,9,6.6453184)),
locate(2,1,R),
red(arc(-2.5,0,5,-5,335,355)), red(arc(-2.5,0,5,-5,265,285)),
red(arc(0,-sqrt(9.75),5,-5,80,100)),red(arc(0,-sqrt(9.75),5,-5,150,170)),
red(line(1.7968751,.87820278,-2.5,0)), red(line(1.7968751,.87820278,0,-sqrt(9.75))) )}}}

Edwin</pre>