5. Given rhombus ABCD, construct the inscribed circle.
Click here for a GSP sketch of the construction.
Click here for a JSP sketch of the construction. NOTE: you will need a java-enabled browser.
Construction:
Given rhombus ABCD. Construct the diagonals and their intersection.
Construct the line perpendicular to side AD through point P. Construct the intersection of this line with segment AD (point E) and segment BC (point F). Construct the line perpendicular to side DC through point P. Construct the intersection of this line with segment DC (point G) and segment AB (point H).
Construct the circle with center at point P and with radius of length = d(PE). This circle is the inscribed circle.
Click here for proof why this construction works.