Steps, such as how to draw a perpendicular to a line, an angle bisector, or a perpendicular bisector of a segment, are skipped in here. Mark point K. From K, draw a horizontal ray rightwards about 12cm long, and mark the right end L. Mark point B on KL about 4cm away from K. Point A will be above BL.
From B, draw a vertical ray upwards about 8cm long, and mark the upper end V. BV intersects KL at right angles, so ∠VBL=90°. Bisect ∠VBL. From B, draw the angle bisector upwards about 10cm long. Mark the upper end M above L, so ∠MBL=45°. Note that the exact length of each line mentioned above is not important.
Mark point A on BM exactly 5.4cm away from B, and point C on BL exactly 4.6cm away from B. Connect A to C. △ABC is the required triangle with AB=5.4cm, BC=4.6cm and ∠ABC=45°.
Draw perpendicular bisectors of AB and BC, and mark the intersection of 2 bisectors O. Draw a circle with its radius OA, and check if the circle passes thru points B and C. CKD. (Because △OAB,△OBC and △OCA are isoscelese, and share the sides of the same length: OA.) Therefore, the circle O is the required one that circumscribes △ABC. (AC=approx. 3.9cm, R=approx. 2.75cm)