Question

Using a ruler and a pair of compasses only, construct a parallelogram ABCD in which/ab/=8cm, abc=135° and the diagonal/ac/=12cm. Without making any calculations, construct a rhombus cdpq equal in area to ABCD with p and q on AB produced. Draw a circle passing through c, d and p, measure the radius of the circle.

Answer 1

Having constructed ABCD, use CD as radius and draw an arc to intersect AB extended at P. Then mark PQ=CD. The rhombus CDPQ has the same base and height as ABCD, so its area is the same.

And of course, C and P are both 8 cm from D, because that's the way we constructed P.